Chapter-4 Quadratic Equations — Online MCQ Test
MATHS · CLASS 10th · Karnataka State Board
Practice Chapter-4 Quadratic Equations with a free chapter-wise online MCQ test.
This chapter covers: Chapter Quadratic Equations.
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Chapter-4 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. 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).
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.
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.
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).
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.
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.