GCSE Solving Quadratic Equations 2

Question 1

What are the solutions to x² - 5x + 6 = 0?

Accepted Answer

x = 2 and x = 3

Answer

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?

Accepted Answer

−8

Answer

Discriminant = b² − 4ac = 16 − 24 = −8.

Question 3

Which of the following equations has exactly one repeated root?

Accepted Answer

x² − 6x + 9 = 0

Answer

x² − 6x + 9 = (x − 3)² = 0 gives the repeated root x = 3.

Question 4

Solve 2x² + 7x + 3 = 0 by factoring.

Accepted Answer

x = −3 and x = −½

Answer

Factoring gives (2x + 1)(x + 3) = 0, so x = −½ or x = −3.

Question 5

What is the vertex form of x² − 4x + 7?

Accepted Answer

(x − 2)² + 3

Answer

Completing the square: x² − 4x + 4 − 4 + 7 = (x − 2)² + 3.

GCSE - General Certificate of Secondary Education Practice Test