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