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All questions of Quadratic Equations & Graphs for SSS 1 Exam

Solve 9x2 = 36​
  • a)
    ±2
  • b)
    ±6
  • c)
    ±4
  • d)
    2
Correct answer is option 'A'. Can you explain this answer?

Nilanjan Shah answered
Solution:
To solve this equation, we need to isolate the variable x.

Given equation is 9x2 = 36

Step 1: Divide both sides by 9
9x2/9 = 36/9

Step 2: Simplify
x2 = 4

Step 3: Take square root on both sides
√(x2) = √4

Step 4: Simplify
x = ±2

Therefore, the solution of the given equation 9x2 = 36 is x = ±2.

Explanation:
The given equation is a quadratic equation in which we need to find the value of x. To solve the equation, we need to isolate the variable x by following the steps mentioned above. We divided both sides by 9 to simplify the equation. After simplification, we got x2 = 4 which means x can be either positive or negative 2. We took the square root of both sides and simplified the equation to get the final solution x = ±2.
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5x2+8x+4 = 2x2+4x+6 is a
  • a)
    linear equation
  • b)
    constant
  • c)
    cubic equation
  • d)
    quadratic equation
Correct answer is option 'D'. Can you explain this answer?

Palak Patel answered
Given: 5x2+8x+4 = 2x2+4x+6
⇒ 5x2−2x2+8x−4x+4−6 = 0
⇒ 3x2+4x−2 = 0
Here, the degree is 2, therefore it is a quadratic equation.

The two consecutive odd positive integers, sum of whose squares is 290 are
  • a)
    13, 15
  • b)
    11, 13
  • c)
    7, 9
  • d)
    5, 7
Correct answer is option 'B'. Can you explain this answer?

Drishti Kumari answered
Let first consecutive odd positive integer be x 
Secon = x + 2 
(x)^2 + ( x + 2 )^2 = 290 
x^2 + x^2 + 4 + 4x = 290 
2x^2 + 4x = 290 - 4 
2x^2 + 4x = 286 
2x^2 + 4x - 286 = 0 
x^2 + 2x - 143 = 0
x^2 + 13x - 11x - 143 = 0 
x ( x + 13 ) - 11 ( x + 13 ) = 0 
( x -11) ( x + 13) = 0 
x = 11 Or  x = -13 
Second = 11 + 2 = 13 
Hence option (B) is correct .

Which of the following in not a quadratic equation:​
  • a)
    (x – 2)2 + 1 = 2x – 3
  • b)
    (x + 2)2 = x3 – 4
  • c)
    x(2x + 3) = x2 + 1
  • d)
    x(x + 1) + 8 = (x + 2) (x – 2)
Correct answer is option 'D'. Can you explain this answer?

Krishna Iyer answered
Option (B) and (D) , both are the correct answers.  We have x(x + 1) + 8 = (x + 2) (x – 2)
=x2 + x + 8 = x2 - 4
= x = -12, which is not a quadratic equation
Also, in (B) (x + 2)2 = x3 – 4
=x2 +4x + 4=x3 - 4, which is a cubic equation

Can you explain the answer of this question below:

 If 4 is a root of the equation , then k is​

  • A:

    -28

  • B:

    -12

  • C:

    12

  • D:

    28

The answer is a.

Arun Sharma answered
4 is the solution , this means that if we put x=4 we get 0. So putting x=4 in the equation x2+3x+k=0 we get 42+3*4+k=0
16+12+k=0 ⇒ k=-28

(x2 + 1)2 - x2 = 0 has
  • a)
    Four real roots
  • b)
    Two real roots
  • c)
    No real roots
  • d)
    One real root
Correct answer is option 'C'. Can you explain this answer?

Arun Sharma answered
Given equation is (x2 + 1)2 - x2 = 0
⇒ x4 + 1 + 2x2 - x2 = 0 [∵ (a + b)2 = a2 + b2 + 2ab]
⇒ x4 + x2 + 1 = 0
Let x2 = y
∴ (x2)2 + x2 + 1 = 0
y2 + y + 1 = 0
On comparing with ay2 + by + c = 0, we get
a = 1, b = 1 and c = 1
Discriminant, D = b2 - 4ac
= (1)2 - 4(1)(1)
= 1 - 4 = -3
Since, D < 0
∴ y2 + y + 1 = 0 i.e., x4 + x2 + 1 = 0 or (x2 + 1)2 - x2 = 0 has no real roots.

The value of q if x = 2 is a solution of 8x2 + qx – 4 = 0 is _____​
  • a)
    14
  • b)
    -28
  • c)
    -14
  • d)
    28
Correct answer is option 'C'. Can you explain this answer?

Kuldeep Raj answered
Let us place 2 in the place of "x" for 8x² + qx - 4 = 0 (According to the question).

8(2)² + q(2) - 4 = 0.

8(4) + 2q - 4 = 0.

32 + 2q - 4 = 0.


Shift (32) to the right side.
2q - 4 = -32.

Shift (-4) to the right side. Then,
2q = -32 + 4.

2q = -28.

q = -28/2.

q = -14.


Therefore, the value of q if x = 2 is a solution of 8x² + qx - 4 = 0 is -14.


Hence, option (c) is correct friend...

The quadratic equation  has
  • a)
    two distinct real roots
  • b)
    two equal real roots
  • c)
    no real root
  • d)
    more than two real roots
Correct answer is option 'C'. Can you explain this answer?

Amit Kumar answered
We have a quadratic equation: 
If we have standard equation ax2 + bx + c  then D = b2 - 4ac
a= 2, b= -√5, c= 1
D = (-√5)2 - (4x2x1)
D= 5 - 8
D = -3
As the value of D<0 so there is no real root

if 1/2  is a root of the equation   then the value of k is
  • a)
    2
  • b)
    -2
  • c)
    1/4
  • d)
    1/2
Correct answer is option 'A'. Can you explain this answer?

Ishan Choudhury answered
As 1/2 is a root then it will satisfy the given equation.
Put x = 1/2
1/4 +(k×1/2) - 5/4 =0
k×1/2 =5/4 -1/4
k =2

Solve for x : 6x2 + 40 = 31x
  • a)
  • b)
  • c)
    0,8/3
  • d)
    None of the above
Correct answer is option 'B'. Can you explain this answer?

Nirmal Kumar answered
6x²-31x+40=0,
a=6,
b=-31,
c=40,
by quadratic formula-->
x=-b±√b²-4ac/2a,
by putting the values of a,b and c, we get,
x=-(-31)±√(-31)²-4(6)(40)/2(6),
=31±√961-960/12,
=31±√1/12,
=31±1/12,
x=30/12or ,32/12,
x=5/2 or, 8/3,
hence , option B is correct

If one root of a Quadratic equation is m + , then the other root is​
  • a)
    m – √n
  • b)
    m +√n
  • c)
    Can not be determined
  • d)
    √m + n
Correct answer is option 'A'. Can you explain this answer?

Arun Sharma answered
In a quadratic equation with rational coefficients has an irrational root  α + √β, then it has a conjugate root α - √β.
So if the root is m+ √n the other root will be m- √n

The nature of the roots of the equation x2 – 5x + 7 = 0 is –
  • a)
    No real roots
  • b)
    1 real root
  • c)
    Can't be determined
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Krishna Iyer answered
Given equation is x2-5x+7=0
We have discriminant as b2-4ac=(-5)2-4*1*7= -3
And x = , Since we do not have any real number which is a root of a negative number, the roots are not real.

If b2 - 4ac = 0 then The roots of the Quadratic equation ax2 + bx + c = 0 are given by :
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'B'. Can you explain this answer?

Udexy Coaching Center answered
Formula for finding the roots of a quadratic equation is

So since 
b2 - 4ac = 0, putting this value in the equation

So there are repeated roots

Read the following text and answer the following questions on the basis of the same:
Nidhi and Ria are very close friends. Nidhi’s parents own a Maruti Alto and Ria’s parents own a Toyota Liva. Both the families decided to go for picnic to Somnath temple in Gujarat by their own cars. Nidhi car travels x km/h when Ria’s car travels 5 km/h more than Nidhi’s car Nidhi’s car took 4 hours more than Ria’s car in covering 400 km.
Q. Which of the following quadratic equations describe the speed of Nidhi’s car?
  • a)
    x2 – 5x – 500 = 0
  • b)
    x2 + 4x – 400 = 0
  • c)
    x2 + 5x – 500 = 0
  • d)
    x2 – 4x + 400 = 0
Correct answer is option 'C'. Can you explain this answer?

Avinash Patel answered
Let Speed of Nidhi = x km/h
Time taken = t + 4 km/h
Time = D/s
Speed of Ria = (x + 5) km/h
Time taken = t hour
According to the question,
⇒
⇒
⇒ x2 + 5x – 500 = 0

Which of the following equations has - 1 as a root?
  • a)
     x2 + 3x - 10 = 0
  • b)
     x2 - x - 12 = 0
  • c)
     3x2 - 2x - 5 = 0
  • d)
     9x2 + 24x + 16 = 0
Correct answer is option 'C'. Can you explain this answer?

Gaurav Kumar answered
3x² - 2x - 5 = 0
3x² + 3x - 5x - 5 = 0
3x(x+1) - 5(x+1) = 0
(x+1)(3x-5) = 0
x = -1 and 5/3.
Hence roots of given polynomial are -1 and 5/3.

Solution of a quadratic equation x²+ 5x - 6 = 0
  • a)
    x = -1, x = 6
  • b)
    x = 1, x = - 6
  • c)
    x = 1
  • d)
    x = 6
Correct answer is option 'B'. Can you explain this answer?

Vikas Kumar answered
x^2 + 5x - 6 = 0
is factored into this:
(x + 6) * (x - 1) = 0

x * (x - 1) + 6 * (x - 1) = 0
x^2 - x + 6x - 6 = 0
x^2 + 5x - 6 = 0

In its factored form, it is easy to see that if either term inside the parentheses can be set to zero, then no matter what it is multiplied by, the equation still results in zero.

If we set x = -6, or 1, then the equation is satisfied. You should go back into the original equation and check your work.
...
x = -6:
-6^2 + 5(-6) - 6 = 0
36 - 30 - 6 = 0
0 = 0 checks
...
x = 1:
1^2 + 5(1) - 6 = 0
1 + 5 - 6 = 0
0 = 0 checks
...
Solutions are x = -6, 1

The two positive numbers differ by 5 and square of their sum is 169 are
  • a)
    2,4
  • b)
    5,6
  • c)
    4,9
  • d)
    3,7
Correct answer is option 'C'. Can you explain this answer?

Apoorv khanna answered
Explanation:
Let the two numbers be x and y, where x is greater than y.
Given, x - y = 5
=> x = y + 5
Also, (x+y)^2 = 169
=> (y+5+y)^2 = 169 (Substituting x = y + 5)
=> (2y+5)^2 = 169
=> 4y^2 + 20y + 25 = 169 (Expanding the square)
=> 4y^2 + 20y - 144 = 0
=> y^2 + 5y - 36 = 0
=> (y + 9)(y - 4) = 0
=> y = -9 or y = 4
Since the numbers are positive, y = 4
Therefore, x = y + 5 = 9
Hence, the two numbers are 4 and 9.
Therefore, option C is the correct answer.

Ruhi’s mother is 26 years older than her. The product of their ages (in years) 3 years from now will be 360. Form a Quadratic equation so as to find Ruhi’s age​
  • a)
    x 2 + 32 x – 273 = 0
  • b)
    x 2 -32 x – 273=0
  • c)
    x 2 + 32 x + 273 = 0
  • d)
    x 2 – 32 x +273 = 0
Correct answer is option 'A'. Can you explain this answer?

Amit Sharma answered
Ruhi’s mother is 26 years older than her
So let Ruhi’s age is x
So mother’s age is x+26
The product of their ages 3 years from now will be 360
So After three years , Ruhi’s age will be x+3
Mother’s age will be x+26+3=x+29
Product of their ages =(x + 3)(x + 29)=360
x2+(3+29)x+87=360
x2+32x-273=0

 The positive root of 217978_image002 is
  • a)
    3
  • b)
    4
  • c)
    5
  • d)
    7
Correct answer is option 'C'. Can you explain this answer?

Neer Shreyansh answered
Hi , The right answer is B because: - √( 3x^2 + 6 ) = 9 Do the square bothsides of the Equation. =} 3x^2 + 6 = 81 =} 3x^2 = 81 - 6 =} 3x^2 = 75 Divide bothsides with 3 =} 3x^2 / 3 = 75/ 3 =} x^2 = 25 Now , =} x = sqrt ( 25 ) =} x = + or - 5 But we need pisitive root , therefore , =} x = 5 I hope this help you That's all🙂

Value(s) of k for which the quadratic equation 2x2 -kx + k = 0 has equal roots is
  • a)
    0
  • b)
    4
  • c)
    8
  • d)
    0 and 8
Correct answer is option 'D'. Can you explain this answer?

Kuldeep Kuldeep answered
Solution:-

Compare given Quadratic equation 2x²-kx+k=0 with ax²+bx+c=0, we get

a = 2,
b = -k , 
c = k,

Discriminant (D) = 0

[ Given roots are equal ]

=> b²-4ac = 0

=> (-k)²-4×2×k=0

=> k²-8k=0

=> k(k-8)=0

=> k = 0 or k=8.

So, option d is correct.

Which of the following equations has no real roots ?
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'A'. Can you explain this answer?

Amit Kumar answered
(a) The given equation is x2 - 4x + 3√2 = 0.
On comparing with ax2 + bx + c = 0, we get
a = 1, b = -4 and c = 3√2
The discriminant of x2 - 4x + 3√2 = 0 is
D = b2 - 4ac
= (-4)2 - 4(1)(3√2) = 16 - 12√2 = 16 - 12 x (1.41)
= 16 - 16.92 = -0.92
⇒ b2 - 4ac < 0
(b) The given equation is x2 + 4x - 3√2 = 0
On comparing the equation with ax2 + bx + c = 0, we get
a = 1, b = 4 and c = -3√2
Then, D = b2 - 4ac = (-4)2 - 4(1)(-3√2)
= 16 + 12√2 > 0
Hence, the equation has real roots.
(c) Given equation is x2 - 4x - 3√2 = 0
On comparing the equation with ax2 + bx + c = 0, we get
a = 1, b = -4 and c = -3√2
Then, D = b2 - 4ac = (-4)2 - 4(1) (-3√2)
= 16 + 12√2 > 0
Hence, the equation has real roots.
(d) Given equation is 3x​2 + 4√3x + 4 = 0.
On comparing the equation with ax2 + bx + c = 0, we get
a = 3, b = 4√3 and c = 4
Then, D = b2 - 4ac = (4√3)2 - 4(3)(4) = 48 - 48 = 0
Hence, the equation has real roots.
Hence, x2 - 4x + 3√2 = 0 has no real roots.

The condition for equation ax2 + bx + c = 0 to be linear is​
  • a)
    a > 0, b = 0
  • b)
    a ≠ 0, b = 0
  • c)
    a < 0, b = 0
  • d)
    a = 0, b ≠ 0
Correct answer is option 'D'. Can you explain this answer?

Tanisha answered
Answer is d...bcoz to make ax^2 +bx+c=0,linear equation.
we need to eliminate ax^2.
So, we will put a=0 ,to make the degree of this equation 1 ...and b should not be equal to 0,bcoz if b will be 0 ,then it will be a constant equation,instead of a linear equation.

The solution of 5z2 = 3z is​
  • a)
    0, 3/5
  • b)
    0, -3/5
  • c)
    3/5
  • d)
    0
Correct answer is option 'A'. Can you explain this answer?

Vikram Kapoor answered
We have 5z2=3z
5z2-3z=0
z(5z-3)=0
So either z=0
Or 5z-3 =0  = z=⅗. So there are two solutions

If a,b,c are real and b2-4ac >0 then roots of equation are​
  • a)
    real roots
  • b)
    real and equal
  • c)
    real and unequal
  • d)
    No real roots
Correct answer is option 'C'. Can you explain this answer?

Ram trivedi answered
The expression b^2 - 4ac is the discriminant of a quadratic equation of the form ax^2 + bx + c = 0. It determines the nature of the solutions of the equation.

If b^2 - 4ac > 0, then the quadratic equation has two distinct real solutions.

If b^2 - 4ac = 0, then the quadratic equation has one real solution (also known as a double root).

If b^2 - 4ac < 0,="" then="" the="" quadratic="" equation="" has="" no="" real="" solutions.="" however,="" it="" may="" have="" two="" complex="" />

So, in summary, if b^2 - 4ac > 0, there are two real solutions.

Two candidates attempt to solve a quadratic equation of the form x2 + px + q = 0. One starts with a wrong
value of p and finds the roots to be 2 and 6. The other starts with a wrong value of q and finds the roots to be 2 and – 9. Find the correct roots of the equation :
  • a)
    3, 4
  • b)
    - 3, - 4
  • c)
    3, – 4
  • d)
    – 3, 4
Correct answer is option 'B'. Can you explain this answer?

Nisha Choudhury answered
If the roots are 2 and 6
then the quadratic equation will be
(x−2)(x−6)=0
⇒x2−6x−2x+12=0
⇒x2−8x+12=0
If the roots are 2 and −9then the quadratic equation will be
(x−2)(x+9)=0
⇒x2+9x−2x−18=0
⇒x2+7x−18=0
Now it is given that
p is wrong in the first quadratic equation and q is right and vice versa for the second quadratic equation
So, p=−8 is wrong and q=12 is right
Similarly p=7 is right and q=−18 is wrong
So taking the correct values of p and qour equation will become
x2+7x+12=0
⇒x2+4x+3x+12=0
⇒x=−3 and x=−4

Which of the following statement is TRUE?
  • a)
    A quadratic equation in variable x is of the form ax2 + bx + c = 0, where a, b, c are real numbers a ≠ o.
  • b)
    If we can factorise ax2 + bx + c, a ≠ 0 into product of two linear factors then roots can be found by equating each factor to zero
  • c)
    A real number R is said to be a root of the quadratic equation ax2 + bx + c = 0 if a(R)2 + bR + c = 0.
  • d)
    All the above
Correct answer is option 'D'. Can you explain this answer?

Anita Menon answered
A quadratic equation in variable x is of the form ax2+ bx + c = 0, where a, b, c are real numbers a ≠ o, because if a=0 then the equation becomes a linear equation.
If we can factorise ax2 + bx + c, a ≠ 0 into product of two linear factors then roots can be found by equating each factor to zero because if two factors are in multiplication and equal to zero then either of the factor is zero.
A real number R is said to be a root of the quadratic equation ax2 + bx + c = 0 if a(R)2 + bR + c = 0. , root means that the value gives answer equal to zero.
So all are correct.

Chapter doubts & questions for Quadratic Equations & Graphs - Mathematics for SSS 1 2024 is part of SSS 1 exam preparation. The chapters have been prepared according to the SSS 1 exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for SSS 1 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

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