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Quadratic Equations Practice Questions

Class 10 · Mathematics · 2025 free MCQs with instant results and detailed explanations.

2025
Total
771
Easy
972
Medium
282
Hard

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Topics in Quadratic Equations

Nature of Roots 539
Completing the Square 423
Quadratic Formula 483
Factorization Method 580

Sample Questions from Quadratic Equations

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Q1
Easy
Which of the following is the correct factorization of the quadratic equation x² - 5x + 6?
A. (x - 2)(x - 3)
B. (x + 2)(x + 3)
C. (x - 1)(x - 6)
D. (x + 1)(x + 6)
Show Answer & Explanation
Correct Answer: A
The quadratic x² - 5x + 6 factors to (x - 2)(x - 3), as -2 and -3 sum to -5 and multiply to 6.
Q2
Easy
Which of the following equations can be factored as (x + 4)(x - 1)?
A. x² + 3x - 4
B. x² + 3x + 4
C. x² - 3x - 4
D. x² + 5x + 4
Show Answer & Explanation
Correct Answer: A
Expanding (x + 4)(x - 1) gives x² + 3x - 4, matching option A.
Q3
Easy
What are the roots of the quadratic equation x² - 8x + 15 = 0, when factored?
A. 3 and 5
B. 2 and 6
C. 1 and 15
D. 5 and 3
Show Answer & Explanation
Correct Answer: A
The factors of 15 that sum to -8 are -3 and -5, giving roots 3 and 5.
Q4
Medium
Which of the following is a correct factorization of the quadratic x² + 4x - 21?
A. (x + 7)(x - 3)
B. (x - 7)(x + 3)
C. (x + 3)(x + 7)
D. (x - 3)(x - 7)
Show Answer & Explanation
Correct Answer: A
The quadratic factors as (x + 7)(x - 3) since 7 and -3 multiply to -21 and add to 4.
Q5
Medium
If the roots of the quadratic equation x² + px + q = 0 are -2 and -3, what is the value of p?
A. -5
B. -6
C. 5
D. 6
Show Answer & Explanation
Correct Answer: A
The sum of the roots (-2) + (-3) = -5 gives p = -5.
Q6
Medium
Which quadratic equation can be factored as (x + 2)(x - 4)?
A. x² - 2x - 8
B. x² + 2x - 8
C. x² - 2x + 8
D. x² + 2x + 8
Show Answer & Explanation
Correct Answer: A
Expanding (x + 2)(x - 4) results in x² - 2x - 8.
Q7
Medium
If the quadratic equation ax² + bx + c = 0 can be factored, what must be true about its discriminant?
A. It must be greater than zero.
B. It must be less than zero.
C. It must be equal to zero.
D. It can be zero or greater than zero.
Show Answer & Explanation
Correct Answer: D
A quadratic can be factored if the discriminant is zero (repeated roots) or positive (two distinct roots).
Q8
Hard
Which of the following quadratic equations can be factored into the form (x - a)(x - b) where a and b are integers?
A. x^2 - 5x + 6
B. x^2 + 3x + 2
C. x^2 + 4x + 5
D. x^2 - 4x + 3
Show Answer & Explanation
Correct Answer: C
The equation x^2 + 4x + 5 has no real roots since the discriminant is negative.
Q9
Hard
If the quadratic equation x^2 - 7x + k = 0 has equal roots, what is the value of k?
A. 12.25
B. 12
C. 14
D. 15
Show Answer & Explanation
Correct Answer: B
For equal roots, the discriminant must be zero: D = b^2 - 4ac = 0. Thus, 49 - 4k = 0 leads to k = 12.
Q10
Hard
Which of the following quadratic expressions can be factored completely over the integers?
A. 2x^2 + 8x + 6
B. 3x^2 - 2x - 8
C. x^2 + 6x + 8
D. x^2 + 4x + 4
Show Answer & Explanation
Correct Answer: D
The expression x^2 + 4x + 4 factors to (x + 2)(x + 2), indicating it is a perfect square.

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Quadratic Equations — Class 10 Mathematics Practice Questions Online

This page contains 2025 practice MCQs for the chapter Quadratic Equations in Class 10 Mathematics. The questions are organized by difficulty — 771 easy, 972 medium, 282 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 4 topics, giving you comprehensive coverage of the entire chapter.