GCSE Solving Quadratic Equations 4

Question 1

Solve 3x² − 12 = 0.

Accepted Answer

x = ±2

Answer

3x² = 12, x² = 4, so x = ±2.

Question 2

Which of these quadratics cannot be solved by factoring over integers?

Accepted Answer

x² + x + 1 = 0

Answer

x² + x + 1 has discriminant = 1 − 4 = −3, so it has no integer factors.

Question 3

The sum of a number and its square is 12. Which equation models this?

Accepted Answer

x² + x − 12 = 0

Answer

x + x² = 12 rearranges to x² + x − 12 = 0.

Question 4

What are the x-intercepts of the graph of y = x² − x − 6?

Accepted Answer

(3, 0) and (−2, 0)

Answer

Setting y = 0: (x − 3)(x + 2) = 0 gives x = 3 or x = −2.

Question 5

Solve 5x² + 5x = 0.

Accepted Answer

x = 0 and x = −1

Answer

Factor as 5x(x + 1) = 0, giving x = 0 or x = −1.

GCSE - General Certificate of Secondary Education Practice Test