GCSE Solving Quadratic Equations 3 — Questions and Answers
Question 1: Solve x² = 49.
- x = ±7 (Correct answer)
- x = 7 only
- x = ±24.5
- x = −7 only
Correct answer: x = ±7
Taking the square root of both sides gives x = 7 or x = −7.
Question 2: Which method is most efficient for solving x² − 9 = 0?
- Difference of two squares (Correct answer)
- Quadratic formula
- Completing the square
- Graphing
Correct answer: Difference of two squares
x² − 9 = (x − 3)(x + 3) = 0 is instantly solved as a difference of squares.
Question 3: What value of k makes x² + kx + 16 = 0 have a repeated root?
- 8 (Correct answer)
- 4
- 16
- −8
Correct answer: 8
For a repeated root, discriminant = 0: k² − 64 = 0, so k = 8 (taking positive value).
Question 4: Using the quadratic formula, solve x² − 3x − 10 = 0.
- x = 5 and x = −2 (Correct answer)
- x = −5 and x = 2
- x = 5 and x = 2
- x = −5 and x = −2
Correct answer: x = 5 and x = −2
x = (3 ± √49) / 2 = (3 ± 7) / 2, giving x = 5 or x = −2.
Question 5: Solve 4x² − 1 = 0.
- x = ±½ (Correct answer)
- x = ±¼
- x = ±1
- x = ±2
Correct answer: x = ±½
4x² = 1, x² = ¼, so x = ±½.
Question 6: Complete the square to solve x² + 6x − 7 = 0.
- x = 1 and x = −7 (Correct answer)
- x = −1 and x = 7
- x = 1 and x = 7
- x = −1 and x = −7
Correct answer: x = 1 and x = −7
(x + 3)² − 16 = 0 → (x + 3)² = 16 → x = 1 or x = −7.
Question 7: If one root of x² + bx + 12 = 0 is x = 3, what is the other root?
- 4 (Correct answer)
- −4
- −3
- 6
Correct answer: 4
By Vieta's formulas, the product of roots = 12, so the other root = 12/3 = 4.
