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All Exams  >   Class 10  >   Mathematics Class 10 (Maharashtra SSC Board)  >   All Questions

All questions of Quadratic Equations for Class 10 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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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?

Rahul Kumar 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.

Vp Classes 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

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 x = 1 is a common root of the equation x2 + ax – 3 = 0 and bx2 – 7x + 2 = 0 then ab =
  • a)
    10
  • b)
    -3
  • c)
    6
  • d)
    7
Correct answer is option 'A'. Can you explain this answer?

Zachary Foster answered
Given:
  • x = 1 is a common root of the equations:
    • x² + ax - 3 = 0
    • bx² - 7x + 2 = 0
To find:
  • The value of ab.
Solution:
Since x = 1 is a root of both equations, we can substitute x = 1 in both equations.
Equation 1:
  • 1² + a(1) - 3 = 0
  • 1 + a - 3 = 0
  • a = 2
Equation 2:
  • b(1)² - 7(1) + 2 = 0
  • b - 7 + 2 = 0
  • b = 5
Therefore, ab = 2 * 5 = 10
So, the value of ab is 10.

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.

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.

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...

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

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

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.

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.

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

Adi2003bro answered
Simplification of LHS x+1/x =. x^2+1/x .transposing deno.x to RHS will give. x(x+1). =. x^2+ x. now combining RHS&LHS . x^2+1=x^2+x . x=1 hence highest power 1 hence not a quad. equ.

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

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.

 If x = 1 is a root of equation x2 – Kx + 5 = 0 then value of K is
  • a)
    4
  • b)
    6
  • c)
    -6
  • d)
    5
Correct answer is option 'B'. Can you explain this answer?

Ananya Das answered
Root of the equation means that the value when substituted in the equation gives zero as answer.
x2 - kx + 5 = 0
Putting x = 1
1*1 -k + 5 = 0
-k+6=0
k=6

Zeroes of the quadratic polynomial ax2 + bx + c and roots of the quadratic equation ax2 + bx + c = 0 are ——–​
  • a)
    Equal to zero
  • b)
    Different
  • c)
    Same
  • d)
    Either same or different
Correct answer is option 'C'. Can you explain this answer?

Aditi bajaj answered
Understanding the Relationship Between Zeroes and Roots
The zeroes of a quadratic polynomial and the roots of its corresponding quadratic equation are intrinsically linked concepts in algebra.
Definition of Zeroes and Roots
- The zeroes of a quadratic polynomial ax² + bx + c are the values of x that make the polynomial equal to zero.
- The roots of the quadratic equation ax² + bx + c = 0 are the solutions to this equation.
Key Connection
- Both terms refer to the same values of x where the polynomial intersects the x-axis. Thus, they are essentially the same mathematical entities expressed in different contexts.
Discriminant Analysis
- The nature of the roots (or zeroes) can be determined using the discriminant (D = b² - 4ac):
- If D > 0: Two distinct real roots (zeroes).
- If D = 0: One real root (zero), indicating the roots are equal.
- If D < 0:="" no="" real="" roots="" (zeroes),="" only="" complex="" />
Conclusion
- The statement that the zeroes of the quadratic polynomial and the roots of the quadratic equation are "same" is correct because they represent the same concept.
- Therefore, option 'C' is the appropriate choice, as both zeroes and roots indicate the values where the polynomial equals zero.
In summary, understanding that the zeroes of a polynomial and the roots of its equation are synonymous is crucial for grasping the fundamentals of quadratic functions.

A shopkeeper buys a number of books for Rs. 80. If he had bought 4 more for the same amount, each book would have cost Re. 1 less. How many books did he buy?
  • a)
    8
  • b)
    16
  • c)
    24
  • d)
    28
Correct answer is option 'B'. Can you explain this answer?

Sonia malhotra answered
Given, a shopkeeper buys a number of books for Rs. 80.

Let the number of books he bought be x.

Then, the cost of each book = 80/x

According to the question, if he had bought 4 more books for the same amount, each book would have cost Re. 1 less.

So, the new number of books he would have bought = x + 4

And, the cost of each book would be = 80/(x+4)

Also, it is given that each book would have cost Re. 1 less, so we can write:

80/x - 1 = 80/(x+4)

Simplifying this equation, we get:

80x + 320 = 80x - x^2 + 4x

Rearranging and simplifying further, we get:

x^2 - 4x - 320 = 0

Factorizing this quadratic equation, we get:

(x - 20)(x + 16) = 0

So, the possible values of x are 20 and -16. But since x represents the number of books he bought, it cannot be negative. Therefore, x = 20.

Hence, the shopkeeper bought 20 books.

The real roots of a quadratic equation  are given by
  • a)
    A
  • b)
    B
  • c)
    C
  • d)
    D
Correct answer is 'D'. Can you explain this answer?

Ishan Choudhury answered
When b2 - 4ac=0 then we have the root as -b/2a.
When  b2-4ac < 0,then the root is a complex root ,since we have a negative number ,for which real square root is not possible.
When b2 - 4ac > 0 then we have a square root of it and hence we have real roots. So the correct answer is b2 - 4ac > 0

The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48. Find their present ages
  • a)
    2 and 18
  • b)
    The situation is not possible
  • c)
    6 and 14
  • d)
    10 and 10
Correct answer is option 'B'. Can you explain this answer?

Ayush Iyer answered
Let's assume the present ages of the two friends are x and y.

According to the given information, the sum of their ages is 20 years.
So, we can write the equation: x + y = 20.

Four years ago, the product of their ages was 48.
So, four years ago, their ages would have been x - 4 and y - 4.
The product of their ages four years ago is: (x - 4)(y - 4) = 48.

Now, let's solve these two equations to find the values of x and y.

Solving the first equation, x + y = 20, we can express x in terms of y:
x = 20 - y.

Substituting the value of x in the second equation, we have:
(20 - y - 4)(y - 4) = 48.

Simplifying this equation, we get:
(16 - y)(y - 4) = 48
16y - 4y - 64 = 48
12y = 112
y = 9.33.

Since y is not a whole number, it means there are no two whole numbers that satisfy the given conditions. Therefore, the situation is not possible.

Hence, the correct answer is option B - The situation is not possible.

If the value of the Discriminant function of a quadratic equation is D = 27, then its roots are
  • a)
    Distinct, Rational
  • b)
    Same Irrational
  • c)
    Distinct, Irrational
  • d)
     Same, Rational
Correct answer is option 'C'. Can you explain this answer?

Roshni chauhan answered
Quadratic equation is a polynomial equation of degree two, which can be written in the form of ax² + bx + c = 0. The discriminant of a quadratic equation is given by D = b² - 4ac. It is a function of the coefficients of the quadratic equation and is used to determine the nature of the roots of the equation.

Distinct and Irrational Roots

If the value of the discriminant is positive and a perfect square, then the roots of the quadratic equation are distinct and rational. If the value of the discriminant is positive but not a perfect square, then the roots of the quadratic equation are distinct and irrational.

Same and Rational Roots

If the value of the discriminant is zero, then the roots of the quadratic equation are same and rational. If the value of the discriminant is negative, then the roots of the quadratic equation are complex conjugates.

Given, D = 27

From the above discussion, we know that if the value of the discriminant is positive and not a perfect square, then the roots of the quadratic equation are distinct and irrational.

Therefore, the correct answer is option C, which states that the roots of the quadratic equation are distinct and irrational.

Chapter doubts & questions for Quadratic Equations - Mathematics Class 10 (Maharashtra SSC Board) 2025 is part of Class 10 exam preparation. The chapters have been prepared according to the Class 10 exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for Class 10 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

Chapter doubts & questions of Quadratic Equations - Mathematics Class 10 (Maharashtra SSC Board) in English & Hindi are available as part of Class 10 exam. Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.

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