Chapter Exam

Chapter-4 Quadratic Equations — Online MCQ Test

Q: What is the standard form of a quadratic equation?

Answer: B. ax² + bx + c = 0, where a ≠ 0 — The standard form of a quadratic equation is ax² + bx + c = 0 where a, b, c are constants and a ≠ 0 (a cannot be zero, otherwise it won't be quadratic).

Q: Which of the following is a quadratic equation?

Answer: B. x² - 5x + 6 = 0 — x² - 5x + 6 = 0 is a quadratic equation because it has the highest power of x as 2 and is in the form ax² + bx + c = 0.

Q: If α and β are roots of x² - 5x + 6 = 0, then α × β equals:

Answer: B. 6 — By Vieta's formula, product of roots = c/a = 6/1 = 6.

Q: If α = 3 + √2 is a root of a quadratic equation with rational coefficients, the other root is:

Answer: A. 3 - √2 — For quadratic equations with rational coefficients, irrational roots of the form p + √q occur in conjugate pairs; so if 3 + √2 is a root, then 3 - √2 must be the other root.

MATHS · CLASS 10 · Andhra State Board

Practice Chapter-4 Quadratic Equations with a free chapter-wise online MCQ test for Andhra State Board CLASS 10 MATHS. This chapter covers: Chapter Quadratic Equations. AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter-4 Quadratic Equations — Important Questions & Answers (FAQ)

Frequently asked questions from Andhra State Board CLASS 10 MATHS — Chapter-4 Quadratic Equations, with answers and explanations. These are sample questions; the exam has its own separate question set.

What is the standard form of a quadratic equation?

A. ax + b = 0
B. ax² + bx + c = 0, where a ≠ 0 ✓
C. ax³ + bx² + c = 0
D. ax² + bx + c = d

Answer: B. ax² + bx + c = 0, where a ≠ 0
The standard form of a quadratic equation is ax² + bx + c = 0 where a, b, c are constants and a ≠ 0 (a cannot be zero, otherwise it won't be quadratic).

Which of the following is a quadratic equation?

A. 2x + 3 = 0
B. x² - 5x + 6 = 0 ✓
C. x³ + 2x = 5
D. 3x - 7 = 2x + 1

Answer: B. x² - 5x + 6 = 0
x² - 5x + 6 = 0 is a quadratic equation because it has the highest power of x as 2 and is in the form ax² + bx + c = 0.

If α and β are roots of x² - 5x + 6 = 0, then α × β equals:

A. 5
B. 6 ✓
C. -6
D. -5

Answer: B. 6
By Vieta's formula, product of roots = c/a = 6/1 = 6.

Compare the two equations: (1) x² - 4 = 0 and (2) x² + 4 = 0. Which statement is true?

A. Both have real roots
B. Equation (1) has real roots; equation (2) does not ✓
C. Equation (2) has real roots; equation (1) does not
D. Neither has real roots

Answer: B. Equation (1) has real roots; equation (2) does not
Equation (1): x² = 4 ⟹ x = ±2 (real roots). Equation (2): x² = -4 (no real roots).

If α = 3 + √2 is a root of a quadratic equation with rational coefficients, the other root is:

A. 3 - √2 ✓
B. -3 - √2
C. 3 + √2
D. -3 + √2

Answer: A. 3 - √2
For quadratic equations with rational coefficients, irrational roots of the form p + √q occur in conjugate pairs; so if 3 + √2 is a root, then 3 - √2 must be the other root.