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All questions of Quadratic Equations for ACT Exam

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If 2x + 5 > 2 + 3x and 2x - 3 ≤ 4x - 5, then x can take which of the following values?
  • a)
    -2
  • b)
    2
  • c)
    4
  • d)
    -4
Correct answer is option 'B'. Can you explain this answer?

Orion Classes answered
2x + 5 > 2 + 3x
5 – 2 > 3x – 2x
3 > x          .......(1)
2x - 3 ≤ 4x - 5
5 – 3 ≤ 4x – 2x
1 ≤ x          .......(2)
From (1) and (2)
x = 1 or 2

Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for "Quadratic Equations" under Quantitative Aptitude. You can practice these practice quizzes as per your speed and improvise the topic. The same topic is covered under various competitive examinations like - CAT, GMAT, Bank PO, SSC and other competitive examinations.
 
Q. Find the roots of the quadratic equation: x2 + 2x - 15 = 0?
  • a)
    -5, 3
  • b)
    3, 5
  • c)
    -3, 5
  • d)
     -3, -5
  • e)
    5, 2
Correct answer is option 'A'. Can you explain this answer?

Shweta Talwar answered
1.multiply 1st term and last term of the eqn: 1*15 =15
2.now, find factors of 15 that sum of those two factors is the middle term of the eqn.
5 and -3 : when multiplied ans is: -15
and when added ans is: +2
3.change the sign of the factors i.e now factors are -5 and 3
therefore ans is: -5 , 3 (option A)

Calculate the least whole number, which when subtracted from both the terms of the ratio 5 : 6 gives a ratio less than 17 : 22.
  • a)
    5
  • b)
    3
  • c)
    2
  • d)
    4
Correct answer is option 'C'. Can you explain this answer?

Ayesha Joshi answered
Given:
Initial ratio = 5 ∶ 6
Final ratio should be less than 17 ∶ 22
Calculation:
Let the least whole number that is needed to be subtracted be a.
According to the question,
(5 - a)/(6 - a) < 17/22
⇒ 5 × 22 - 22a < 17 × 6 - 17a 
⇒ 110 - 22a < 102 - 17a 
⇒ 110 - 102 < - 17a + 22a 
⇒ 8 < 5a 
⇒ 8/5 = 1.6 < a 
∴ The least whole number must be 2.

ax2 + bx + c > 0 is __________
  • a)
    double inequality
  • b)
    quadratic inequality
  • c)
    numerical inequality
  • d)
    linear inequality
Correct answer is option 'B'. Can you explain this answer?

Orion Classes answered
  • Since it has highest power of x ‘2’ and has inequality sign so, it is called quadratic inequality.
  • It is not numerical inequality as it does not have numbers on both sides of inequality.
  • It does not have two inequality signs so it is not double inequality.

In the Maths Olympiad of 2020 at Animal Planet, two representatives from the donkey’s side, while solving a quadratic equation, committed the following mistakes: (i) One of them made a mistake in the constant term and got the roots as 5 and 9. (ii) Another one committed an error in the coefficient of x and he got the roots as 12 and 4.But in the meantime, they realised that they are wrong and they managed to get it right jointly. Find the quadratic equation.
  • a)
    x2 + 4x + 14 = 0
  • b)
    2x2 + lx - 24 = 0
  • c)
    x2 - 14x + 48 = 0
  • d)
    3x2 - 17x + 52 = 0
Correct answer is option 'C'. Can you explain this answer?

Dhruv Mehra answered
STUDENT 1:

Roots: 5,9.

Hence, x= 5..or x=9

or, x-5 = 0 or x - 9 = 0

or, (x - 5)(x - 9) = 0

or, x2 - 14x + 45 = 0

STUDENT 2:

Roots: 12,4

Hence, x= 12..or x=4

or, x - 12 = 0 or x - 4 = 0

or, (x - 12)(x - 4) = 0

or, x2 - 14x + 48 = 0

ax + b > 0 is ___________
  • a)
    double inequality
  • b)
    quadratic inequality
  • c)
    numerical inequality
  • d)
    linear inequality
Correct answer is option 'D'. Can you explain this answer?

Sofia Bennett answered


Linear Inequality:

Linear inequality is an inequality that involves a linear function. In this case, the inequality ax + b > 0 is a linear inequality because it involves a linear function (ax) and a constant term (b).

Main Characteristics of a Linear Inequality:

- In a linear inequality, the highest power of the variable is 1.
- The graph of a linear inequality forms a straight line.
- The solution set of a linear inequality is usually a half-plane.

Explanation of the Given Inequality:

The given inequality ax + b > 0 is a linear inequality because it involves a linear function (ax) and a constant term (b). The inequality states that the expression ax + b is greater than 0. This means that for the inequality to hold true, the values of x must satisfy the condition that ax + b is greater than 0.

Conclusion:

Therefore, the given inequality ax + b > 0 is classified as a linear inequality because it involves a linear function and a constant term, and the solution set forms a half-plane on a graph.

If x + 2y ≤ 3, x > 0 and y > 0, then one of the solution is
  • a)
    x = -1, y = 2
  • b)
    x = 2, y = 1
  • c)
    x = 1, y = 1
  • d)
    x = 0, y = 0
Correct answer is option 'C'. Can you explain this answer?

Matthew Cox answered
Given Inequalities:
- x + 2y ≤ 3
- x > 0
- y > 0

Solution:

Step 1: Find the possible values of x and y
- From the inequality x + 2y ≤ 3, we can rearrange it to get x ≤ 3 - 2y.
- Since x > 0, we have 0 < x="" ≤="" 3="" -="" />
- Since y > 0, we can also say that y > 0.

Step 2: Determine the possible solutions
- Now, we need to find the values of x and y that satisfy the given conditions.
- Let's start by trying out the options:
- Option 'A': x = -1, y = 2
- Option 'B': x = 2, y = 1
- Option 'C': x = 1, y = 1
- Option 'D': x = 0, y = 0
- Checking each option:
- Option 'A': x = -1, y = 2
- x is not greater than 0, so this option is invalid.
- Option 'B': x = 2, y = 1
- x is greater than 0, but the inequality x + 2y ≤ 3 is not satisfied.
- Option 'C': x = 1, y = 1
- Both x and y are greater than 0, and x + 2y ≤ 3 is satisfied.
- Therefore, this option is a valid solution.
- Option 'D': x = 0, y = 0
- x is not greater than 0, so this option is invalid.

Conclusion:
- The correct solution is x = 1, y = 1, as it satisfies all the given conditions and the inequality.

The roots of the equation 3x2 - 12x + 10 = 0 are?
  • a)
    rational and unequal
  • b)
     complex
  • c)
    real and equal
  • d)
    irrational and unequal
  • e)
    rational and equal
Correct answer is option 'D'. Can you explain this answer?

Gowri Chakraborty answered
The discriminant of the quadratic equation is (-12)2 - 4(3)(10) i.e., 24. As this is positive but not a perfect square, the roots are irrational and unequal.

The expression x2 + kx + 9 becomes positive for what values of k (given that x is real)?
  • a)
    k < 6
  • b)
    k > 6
  • c)
    |K|<6
  • d)
    |k|< 6
Correct answer is option 'C'. Can you explain this answer?

Om Desai answered
Method to Solve :

If the roots are equal(double root) it means that discriminant of quadratic equation b^2-4ac=0
general form of quadratic equation is ax^2+bx+c=0
in this case a=1 b=k and c=9
b^2-4ac=0 then:

k^2-36=0
(k-6)(k+6)=0
k=6 or k=-6
For k=6 or k= -6 given equation has real and equal roots

Find the minimum value of the expression (p +1/p); p > 0.
  • a)
    1
  • b)
    0
  • c)
    2
  • d)
    Depends upon the value of p
Correct answer is option 'C'. Can you explain this answer?

Pallabi Deshpande answered
It should be p. 
Let's try plugging in some values for p. 
First let's take p=0.1 -> 0.1+1/0.1 = 0.1+10/1 = 10.1 
Now let's take p=1 -> 1+1/1 = 2 (smaller Wink ) 
Now let's take p=2 -> 2+2/1 = 4 (bigger again) 

Therefore we know that the values will decrease if you plug in a number between ]0;1[, that the value will be minimum at 1 and later increase again.

If P and Q are the roots of f(x) = x2 - 14x + 45, then find the value of (1/P +1/Q)
  • a)
    45/14
  • b)
    14/45
  • c)
    41/54
  • d)
    54/41
Correct answer is option 'B'. Can you explain this answer?

Prerna Gupta answered
To find the value of (1/P + 1/Q), we need to determine the values of P and Q first.

Given that P and Q are the roots of the quadratic equation f(x) = x^2 - 14x + 45, we can use the quadratic formula to find their values.

The quadratic formula states that for a quadratic equation of the form ax^2 + bx + c = 0, the roots can be found using the formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In our case, a = 1, b = -14, and c = 45. Plugging these values into the quadratic formula, we get:

P = (-(-14) ± √((-14)^2 - 4(1)(45))) / (2(1))
= (14 ± √(196 - 180)) / 2
= (14 ± √16) / 2
= (14 ± 4) / 2
= (18 / 2) or (10 / 2)
= 9 or 5

So, P can have the value of either 9 or 5.

Now, let's find the value of Q. Since P and Q are the roots of the quadratic equation, if P = 9, then Q = 5, and vice versa.

Now, we can calculate (1/P + 1/Q) using the values of P and Q that we found.

(1/P + 1/Q) = (1/9 + 1/5)

To add these fractions, we need a common denominator. The least common denominator of 9 and 5 is 45. We can rewrite the fractions with the common denominator:

(1/P + 1/Q) = (5/45 + 9/45)

Now, we can add the fractions:

(1/P + 1/Q) = (5 + 9) / 45
= 14 / 45

Therefore, the value of (1/P + 1/Q) is 14/45, which corresponds to option B.

If the roots of the equation (a2 + b2) x2 - 2b(a + c) x + (b2 + c2) = 0 are equal then a, b, c, are in
  • a)
    AP
  • b)
    GP
  • c)
    HP
  • d)
    Cannot be said
Correct answer is option 'B'. Can you explain this answer?

Aarav Sharma answered
Explanation:

To find the relation between a, b, and c when the roots of the given equation are equal, let's analyze the equation step by step.

Given equation: (a^2 - b^2)x^2 - 2b(a - c)x + (b^2 - c^2) = 0

Step 1:
When the roots of a quadratic equation are equal, the discriminant of the equation is equal to zero.

Step 2:
The discriminant of a quadratic equation ax^2 + bx + c = 0 is given by the expression b^2 - 4ac.

Step 3:
In the given equation, the discriminant is: (-2b(a - c))^2 - 4(a^2 - b^2)(b^2 - c^2)

Step 4:
To simplify the expression, let's expand the terms and then simplify:

(-2b(a - c))^2 - 4(a^2 - b^2)(b^2 - c^2)
= 4b^2(a - c)^2 - 4(a^2 - b^2)(b^2 - c^2)
= 4b^2(a^2 - 2ac + c^2) - 4(a^2 - b^2)(b^2 - c^2)
= 4b^2a^2 - 8b^2ac + 4b^2c^2 - 4a^2b^2 + 8ac^2 - 4b^2c^2
= 4b^2a^2 - 4a^2b^2 + 8ac^2 - 8b^2ac + 4b^2c^2 - 4b^2c^2
= 4(a^2b^2 - a^2b^2 + 2ac^2 - 2b^2ac)
= 4(2ac^2 - 2b^2ac)
= 8ac^2 - 8ab^2c

Step 5:
Setting the discriminant equal to zero, we have:

8ac^2 - 8ab^2c = 0

Step 6:
Factor out 8ac from the equation:

8ac(c - b^2) = 0

Step 7:
For the equation to be true, either 8ac = 0 or (c - b^2) = 0.

Step 8:
If 8ac = 0, it implies either a = 0 or c = 0.

Step 9:
If (c - b^2) = 0, it implies c = b^2.

Conclusion:
From the above analysis, we can conclude that a, b, and c are in a geometric progression (GP) when the roots of the given equation are equal. Therefore, the correct answer is option 'B' (GP).

The sum of the squares of two consecutive positive integers exceeds their product by 91. Find the integers?
  • a)
    9, 10
  • b)
     10, 11
  • c)
    11, 12
  • d)
    12, 13
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Dhruv Mehra answered
Let the two consecutive positive integers be x and x + 1
x2 + (x + 1)2 - x(x + 1) = 91
x2 + x - 90 = 0
(x + 10)(x - 9) = 0 => x = -10 or 9.
As x is positive x = 9
Hence the two consecutive positive integers are 9 and 10.

For what value of b and c would the equation x2 + bx + c = 0 have roots equal to b and c.
  • a)
    (0,0)
  • b)
    (1,-2)
  • c)
    (1,2)
  • d)
    Both (a) and (b)
Correct answer is option 'D'. Can you explain this answer?

Aarav Sharma answered
To find the values of b and c that would make the equation x^2 + bx + c = 0 have roots equal to b and c, we can use the fact that the sum and product of the roots of a quadratic equation are related to its coefficients.

The sum of the roots of a quadratic equation ax^2 + bx + c = 0 is given by -b/a, and the product of the roots is given by c/a.

In this case, we are given that the roots are b and c. So we have the following equations:

b + c = -b/a
bc = c/a

We can simplify the second equation by multiplying both sides by a:

abc = c

Now we have two equations:

b + c = -b/a
abc = c

We can solve these equations to find the values of b and c.

Solving the equations:
To solve the first equation, we can multiply both sides by a:

ab + ac = -b

Rearranging the equation, we get:

ab + b = -ac

Factoring out b, we have:

b(a + 1) = -ac

Dividing both sides by (a + 1), we get:

b = -ac/(a + 1)

Substituting this value of b into the second equation, we have:

abc = c

Replacing b with -ac/(a + 1), we get:

-a^2c/(a + 1) = c

Cross-multiplying, we have:

-a^2c = c(a + 1)

Simplifying, we get:

-a^2c = ac + c

Adding ac to both sides, we have:

ac - a^2c = c

Factoring out c, we get:

c(a - a^2) = c

Dividing both sides by c, we get:

a - a^2 = 1

This is a quadratic equation in terms of a. We can solve it by rearranging and factoring:

a^2 - a + 1 = 0

This equation does not have any real solutions. Therefore, there are no values of b and c that would make the equation x^2 + bx + c = 0 have roots equal to b and c.

Thus, the correct answer is option D) Both (a) and (b).

The two numbers whose sum is 27 and their product is 182 are
  • a)
    12 and 13
  • b)
    12 and 15
  • c)
    14 and 15
  • d)
    13 and 14
Correct answer is option 'D'. Can you explain this answer?

Prateek Gupta answered
Explanation:Let the one number be xx .As the sum  of numbers is 27 , then the other number will be (27−x)(27−x)                                                                                                                                    According to question

The product of two successive integral multiples of 5 is 1050. Then the numbers are
  • a)
    35 and 40
  • b)
    25 and 30
  • c)
    25 and 42
  • d)
    30 and 35
Correct answer is option 'D'. Can you explain this answer?

Prateek Gupta answered
Explanation:
Let one multiple of 5 be x then the next consecutive multiple of will be (x+5) According to question,
Then the number are 30 and 35.

I. a2 + 8a + 16 = 0,
II. b2 - 4b + 3 = 0 to solve both the equations to find the values of a and b?
  • a)
    If a < b
  • b)
    If a ≤ b
  • c)
    If the relationship between a and b cannot be established
  • d)
    If a > b
  • e)
    If a ≥ b
Correct answer is option 'A'. Can you explain this answer?

Sagar Sharma answered
I. To solve the equation a^2 + 8a + 16 = 0, we can use the quadratic formula:

a = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = 8, and c = 16. Plugging these values into the quadratic formula:

a = (-8 ± √(8^2 - 4(1)(16))) / (2(1))

Simplifying:

a = (-8 ± √(64 - 64)) / 2

a = (-8 ± √0) / 2

a = -8 / 2

a = -4

So, the value of a is -4.

II. To solve the equation b^2 - 4b + 3 = 0, we can factorize it:

(b - 1)(b - 3) = 0

Setting each factor equal to zero:

b - 1 = 0 or b - 3 = 0

b = 1 or b = 3

So, the values of b are 1 and 3.

Therefore, the values of a and b are -4, 1, and 3.

For all x, x2 + 2ax + (10 − 3a) > 0, then the interval in which a lies, is?
  • a)
    a < -5
  • b)
    a > 5
  • c)
    -5 < a < 2
  • d)
    2 < a < 5
  • e)
    a < -2
Correct answer is option 'C'. Can you explain this answer?

Rahul Mehta answered
In f(x) = ax2 + bx + c
When a > 0 and D < 0
Then f(x) is always positive.
x2 + 2ax + 10 − 3a > 0, ∀x ∈ R
⇒ D < 0
⇒ 4a2 − 4(10 − 3a) < 0
⇒ a2 + 3a − 10 < 0
⇒ (a+5)(a−2) < 0
⇒ a ∈ (−5,2)

Which of the following has two distinct roots?
  • a)
    x2+x−5=0
  • b)
    x2+x+5=0
  • c)
    none of these
  • d)
    5x2−3x+1=0
Correct answer is option 'A'. Can you explain this answer?

Siddharth Pillai answered
To determine which of the given options has two distinct roots, we need to determine the discriminant of each equation. The discriminant is the part of the quadratic formula inside the square root, and it helps us determine the nature of the roots of a quadratic equation.

The quadratic equation is of the form ax^2 + bx + c = 0, where a, b, and c are constants.

The discriminant, denoted by Δ, is given by the formula Δ = b^2 - 4ac.

If Δ > 0, the equation has two distinct real roots.
If Δ = 0, the equation has two equal real roots.
If Δ < 0,="" the="" equation="" has="" no="" real="" />

Let's calculate the discriminant for each option:

a) x^2 + x + 5 = 0
In this case, a = 1, b = 1, and c = 5.
Δ = (1)^2 - 4(1)(5) = 1 - 20 = -19 (negative)
Since the discriminant is negative, this equation has no real roots.

b) x^2 + x * 5 = 0
In this case, a = 1, b = 5, and c = 0.
Δ = (5)^2 - 4(1)(0) = 25 - 0 = 25 (positive)
Since the discriminant is positive, this equation has two distinct real roots.

c) 5x^2 + 3x + 1 = 0
In this case, a = 5, b = 3, and c = 1.
Δ = (3)^2 - 4(5)(1) = 9 - 20 = -11 (negative)
Since the discriminant is negative, this equation has no real roots.

Therefore, the only option that has two distinct roots is option 'A' (x^2 + x + 5 = 0).

The expression a2 + ab + b2 is _________for a < 0, b < 0
  • a)
    ≠ 0
  • b)
    <0
  • c)
    > 0
  • d)
    = 0
Correct answer is option 'C'. Can you explain this answer?

Aarya Kumar answered
For a, b negative the given expression will always be positive since, a2, b2 and ab are all positive.

If the roots of the equation (a2 + b2)x2 − 2b(a + c)x + (b2+c2) = 0 are equal then 
  • a)
    2b = ac
  • b)
    b2 = ac
  • c)
    b = 2ac/(a + c)
  • d)
    b = ac
  • e)
    b = 2ac
Correct answer is option 'B'. Can you explain this answer?

Ritika Choudhury answered
(a2 + b2)x2 − 2b(a + c)x + (b2+c2) = 0
Roots are real and equal ∴ D = 0
D = b2 − 4ac = 0
⇒ [−2b(a+c)]2 − 4(a2 + b2)(b2 + c2) = 0
⇒ b2(a2 + c2 + 2ac) −(a2b2 + a2c2 + b4 + c2c2) = 0
⇒ b2a2 + b2c2 + 2acb2 − a2b2 − a2c2 − b4 − b2c2 = 0
⇒ 2acb2 − a2c2 − 2acb2 = 0
⇒ (b2 − ac)2 = 0
⇒ b2 = ac

If the roots of the equation 2x2 - 5x + b = 0 are in the ratio of 2:3, then find the value of b?
  • a)
    3
  • b)
    4
  • c)
    5
  • d)
    6
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Sounak Malik answered
Let the roots of the equation 2a and 3a respectively.
2a + 3a = 5a = -(- 5/2) = 5/2 => a = 1/2
Product of the roots: 6a2 = b/2 => b = 12a2
a = 1/2, b = 3.

If the roots of the equation x2 – 15x2 + kx – 45 = 0 are in A.P., find value of k:
  • a)
    56
  • b)
    59
  • c)
    -56
  • d)
    -59
Correct answer is option 'B'. Can you explain this answer?

KP Classes answered
∵ Roots are in A.R
Let roots are a – d; a; a + d
So, (a – d)+a + (a + d) = 15
or; 3a = 15
or; a = 5
And Product of roots
(a – d ). a . (a + d ) = 45
or (5 – d);5. (5 + d) = 45
or 25 – d2 = 9
or; d2 = 25 – 9 = 16
or; d = √16 = 4
Hence; roots are
a – d, a, a + d = 5 – 4; 5; 5 + 4
= 1; 5 ; 9.
The value of K
= Sum of product of two roots in a order
= (1 × 5) + (5 × 9) + (9 × 1)
= 5 + 45 + 9 = 59
(b) is correct.

A man could buy a certain number of notebooks for Rs.300. If each notebook cost is Rs.5 more, he could have bought 10 notebooks less for the same amount. Find the price of each notebook?
  • a)
    10
  • b)
    8
  • c)
    15
  • d)
    7.50
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Nikita Singh answered
Explanation:
Let the price of each note book be Rs.x.
Let the number of note books which can be brought for Rs.300 each at a price of Rs.x be y.
Hence xy = 300
=> y = 300/x 
(x + 5)(y - 10) = 300 => xy + 5y - 10x - 50 = xy
=>5(300/x) - 10x - 50 = 0 => -150 + x2 + 5x = 0
multiplying both sides by -1/10x
=> x2 + 15x - 10x - 150 = 0
=> x(x + 15) - 10(x + 15) = 0
=> x = 10 or -15
As x>0, x = 10.

 
If one root of the equation ax2+bx+c=0 is three times the other, then b2:ac=
  • a)
    3 : 1
  • b)
    16 : 3
  • c)
    3 : 16
  • d)
    16 : 1
Correct answer is option 'B'. Can you explain this answer?

Aarav Sharma answered
To solve this problem, let's assume that the roots of the quadratic equation ax^2 + bx + c = 0 are x and 3x, where x is a constant.

Finding the sum and product of the roots:
The sum of the roots is given by the formula -b/a, and the product of the roots is given by the formula c/a.

So, the sum of the roots (x + 3x) is -b/a, which simplifies to 4x = -b/a.

Similarly, the product of the roots (x * 3x) is c/a, which simplifies to 3x^2 = c/a.

Finding the ratio of b^2 to ac:
We need to find the ratio b^2 : ac.

Substituting the value of 4x for -b/a in the equation 4x = -b/a, we get:
b = -4ax.

Now, substituting the value of 3x^2 for c/a in the equation 3x^2 = c/a, we get:
c = 3ax^2.

Substituting these values of b and c into the ratio b^2 : ac, we get:
(-4ax)^2 : (3ax^2)(a)
(16a^2x^2) : (3a^2x^2)
16 : 3.

Therefore, the ratio of b^2 to ac is 16 : 3.

Thus, the correct answer is option B) 16 : 3.

The sum of reciprocals of Sharma’s age 3 years ago and 5 years from now is 1/3, then his present age is
  • a)
    7 years
  • b)
    6 years
  • c)
    10 years
  • d)
    8 years
Correct answer is option 'A'. Can you explain this answer?

Sagar Sharma answered
Given:
The sum of reciprocals of Sharma's age 3 years ago and 5 years from now is 1/3.

To find:
Sharma's present age.

Solution:

Let's assume Sharma's present age is x years.

Reciprocals:
The reciprocal of a number is obtained by dividing 1 by the number.

So, the reciprocal of Sharma's age 3 years ago would be 1/(x-3) and the reciprocal of Sharma's age 5 years from now would be 1/(x+5).

Equation:
According to the given information, the sum of these reciprocals is equal to 1/3:

1/(x-3) + 1/(x+5) = 1/3

Multiplying through by the common denominator:

3[(x+5) + (x-3)] = (x-3)(x+5)

Simplifying the equation:

3(2x + 2) = x^2 + 2x - 15

6x + 6 = x^2 + 2x - 15

Rearranging the terms:

x^2 - 4x - 21 = 0

Factoring the quadratic equation:

(x - 7)(x + 3) = 0

Setting each factor equal to zero:

x - 7 = 0 or x + 3 = 0

Solving for x:

x = 7 or x = -3

Conclusion:
Since age cannot be negative, Sharma's present age is 7 years (Option A).

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