Chapter Exam

Chapter 5: 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 real numbers and a ≠ 0. The condition a ≠ 0 ensures the equation is quadratic, not linear.

Q: Which of the following is a quadratic equation?

Answer: B. x² - 5x + 6 = 0 — x² - 5x + 6 = 0 is a quadratic equation as it contains the variable with highest power 2. Option A is linear, C is cubic, and D is not a polynomial equation.

Q: If the discriminant of a quadratic equation is negative, then the equation has:

Answer: C. No real roots (two complex roots) — When discriminant Δ = b² - 4ac < 0, the quadratic equation has no real roots; instead, it has two complex conjugate roots.

Q: The sum of roots of the equation 3x² - 12x + 5 = 0 is:

Answer: A. 4 — For ax² + bx + c = 0, sum of roots = -b/a. Here, sum = -(-12)/3 = 12/3 = 4. (Vieta's formula for sum of roots)

Q: Consider the equation (x - a)² + (x - b)² = 0, where a and b are real constants. Which statement is true?

Answer: B. It has real roots only when a = b — Expanding: 2x² - 2(a+b)x + (a² + b²) = 0. For real roots, discriminant Δ = 4(a+b)² - 8(a² + b²) ≥ 0, which simplifies to 2ab ≤ 0. For real roots with the given form, we need a = b = 0 or both equal.

MATHS · CLASS 10th · Telangana State Board

Practice Chapter 5: Quadratic Equations with a free chapter-wise online MCQ test for Telangana State Board CLASS 10th MATHS. This chapter covers: Exploring second-degree polynomial equations. AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter 5: Quadratic Equations — Important Questions & Answers (FAQ)

Frequently asked questions from Telangana State Board CLASS 10th MATHS — Chapter 5: 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. a + bx + cx² = 0

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 real numbers and a ≠ 0. The condition a ≠ 0 ensures the equation is quadratic, not linear.

Which of the following is a quadratic equation?

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

Answer: B. x² - 5x + 6 = 0
x² - 5x + 6 = 0 is a quadratic equation as it contains the variable with highest power 2. Option A is linear, C is cubic, and D is not a polynomial equation.

If the discriminant of a quadratic equation is negative, then the equation has:

A. Two distinct real roots
B. Two equal real roots
C. No real roots (two complex roots) ✓
D. One root only

Answer: C. No real roots (two complex roots)
When discriminant Δ = b² - 4ac < 0, the quadratic equation has no real roots; instead, it has two complex conjugate roots.

The sum of roots of the equation 3x² - 12x + 5 = 0 is:

A. 4 ✓
B. -4
C. 12
D. 5/3

Answer: A. 4
For ax² + bx + c = 0, sum of roots = -b/a. Here, sum = -(-12)/3 = 12/3 = 4. (Vieta's formula for sum of roots)

Consider the equation (x - a)² + (x - b)² = 0, where a and b are real constants. Which statement is true?

A. It always has two distinct real roots
B. It has real roots only when a = b ✓
C. It is never a quadratic equation
D. It always has complex roots regardless of a and b

Answer: B. It has real roots only when a = b
Expanding: 2x² - 2(a+b)x + (a² + b²) = 0. For real roots, discriminant Δ = 4(a+b)² - 8(a² + b²) ≥ 0, which simplifies to 2ab ≤ 0. For real roots with the given form, we need a = b = 0 or both equal.