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Class 10 Maths Chapter 4: Quadratic Equations MCQs with answers

10 multiple-choice questions on Quadratic Equations, each with its answer and the reason, written from the NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter.

Question 1
Which of the following is a quadratic equation?
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Answer: (c) 3x2 = 0

3x2 = 0 is ax2 + bx + c = 0 with a = 3, b = 0, c = 0; only a must be non-zero. (x + 1)2 = x2 + 4 simplifies to 2x − 3 = 0, which is linear.

Question 2
After simplifying, the equation (x + 3)2 = x(x − 2) + 5 is
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Answer: (d) a linear equation

x2 + 6x + 9 = x2 − 2x + 5. The x2 terms cancel, leaving 8x + 4 = 0, which is linear.

Question 3
When (x − 1)3 = x3 + 2 is simplified, it becomes
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Answer: (b) x2 − x + 1 = 0

x3 − 3x2 + 3x − 1 = x3 + 2 gives −3x2 + 3x − 3 = 0; dividing by −3, x2 − x + 1 = 0. The x3 terms cancel, so it is quadratic.

Question 4
Which of the following is NOT a quadratic equation?
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Answer: (d) (x + 1)3 = 2x(x2 + 1)

In (d) the left side has x3 and the right side 2x3; they do not cancel, and the equation becomes −x3 + 3x2 + x + 1 = 0, a cubic. The others reduce to 3x2 + 3x − 1 = 0, x2 − 6x + 8 = 0 and x2 + 3x − 1 = 0.

Question 5
If x = 2 is a root of x2 + kx − 10 = 0, then k is
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Answer: (a) 3

Substitute x = 2: 4 + 2k − 10 = 0, so 2k = 6 and k = 3.

Question 6
Which of the following is a root of 3x2 − 7x + 2 = 0?
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Answer: (c) 13

3(1/3)2 − 7(1/3) + 2 = 1/3 − 7/3 + 6/3 = 0. The equation factorises as (3x − 1)(x − 2) = 0, roots 1/3 and 2.

Question 7
A quadratic equation has
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Answer: (c) at most two roots

A quadratic polynomial has at most two zeroes, so a quadratic equation has at most two roots.

Question 8
The solution of x2x − 3 = 9x − 3 is
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Answer: (b) x = −3 only

Multiplying by (x − 3) gives x2 = 9, so x = 3 or x = −3. But x = 3 makes the denominator zero in the given equation, so it is rejected; the solution is x = −3.

Question 9
To factorise 6x2 + 7x − 3 by splitting the middle term, 7x is written as
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Answer: (a) 9x − 2x

ac = 6 × (−3) = −18 and b = 7. Since ac < 0 the parts have opposite signs: 9 × (−2) = −18 and 9 + (−2) = 7.

Question 10
The roots of (3x − 2)(x + 4) = 0 are
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Answer: (d) 23 and −4

Set each factor to zero: 3x − 2 = 0 gives x = 2/3; x + 4 = 0 gives x = −4.

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