GCSE Solving Quadratic Equations 2 — Questions and Answers
Question 1: What are the solutions to x² - 5x + 6 = 0?
- x = 2 and x = 3 (Correct answer)
- x = -2 and x = -3
- x = 1 and x = 6
- x = -1 and x = -6
Correct answer: x = 2 and x = 3
Factoring gives (x − 2)(x − 3) = 0, so x = 2 or x = 3.
Question 2: Using the quadratic formula, what is the discriminant of 3x² - 4x + 2 = 0?
- −8 (Correct answer)
- 8
- −4
- 28
Correct answer: −8
Discriminant = b² − 4ac = 16 − 24 = −8.
Question 3: Which of the following equations has exactly one repeated root?
- x² − 6x + 9 = 0 (Correct answer)
- x² − 6x + 8 = 0
- x² − 6x + 5 = 0
- x² − 6x + 10 = 0
Correct answer: x² − 6x + 9 = 0
x² − 6x + 9 = (x − 3)² = 0 gives the repeated root x = 3.
Question 4: Solve 2x² + 7x + 3 = 0 by factoring.
- x = −3 and x = −½ (Correct answer)
- x = 3 and x = ½
- x = −3 and x = ½
- x = 3 and x = −½
Correct answer: x = −3 and x = −½
Factoring gives (2x + 1)(x + 3) = 0, so x = −½ or x = −3.
Question 5: What is the vertex form of x² − 4x + 7?
- (x − 2)² + 3 (Correct answer)
- (x + 2)² + 3
- (x − 2)² − 3
- (x + 2)² − 3
Correct answer: (x − 2)² + 3
Completing the square: x² − 4x + 4 − 4 + 7 = (x − 2)² + 3.
Question 6: How many real solutions does x² + 4 = 0 have?
- None (Correct answer)
- One
- Two
- Four
Correct answer: None
x² = −4 has no real solutions because a square cannot be negative.
Question 7: A square has side length (x − 2). Its area equals 3x + 2. What positive value of x satisfies this?
- 8 (Correct answer)
- 6
- 4
- 10
Correct answer: 8
Expanding gives x² − 4x + 4 = 3x + 2, leading to x² − 7x + 2 = 0; the positive root is approximately x = 8.
GCSE Solving Quadratic Equations 2
What are the solutions to x² - 5x + 6 = 0?