GCSE - General Certificate of Secondary Education Solving Quadratic Equations Questions and Answers

Question 1

A rectangular garden has a length that is 5 metres longer than its width. If the area of the garden is 84 m², what is the width of the garden?

Accepted Answer

7 m

Answer

12 m

Answer

14 m

Answer

5 m

Question 2

Which of the following are the solutions to the quadratic equation 2x² - 5x - 3 = 0?

Accepted Answer

x = 3 and x = -0.5

Answer

x = -3 and x = 0.5

Answer

x = 3 and x = -2

Answer

x = 1.5 and x = -1

Question 3

A student is solving the quadratic equation x² + 8x - 7 = 0 by completing the square. Which of the following shows the equation correctly rewritten in the form (x + p)² = q?

Accepted Answer

(x + 4)² = 23

Answer

(x + 4)² = 9

Answer

(x + 8)² = 71

Answer

(x - 4)² = 23

Question 4

Using the quadratic formula, what are the solutions to 3x² + 7x - 1 = 0? Give your answers correct to 2 decimal places.

Accepted Answer

x = 0.14 and x = -2.47

Answer

x = -0.14 and x = 2.47

Answer

x = 0.15 and x = -2.15

Answer

x = 2.33 and x = -1.00

Question 5

How many distinct real solutions does the quadratic equation 4x² - 12x + 9 = 0 have?

Accepted Answer

One

Answer

Two

Answer

None

Answer

Infinitely many

Question 6

Solve the equation x² - 11x + 18 = 0 by factorising.

Accepted Answer

x = 2 and x = 9

Answer

x = -2 and x = -9

Answer

x = 3 and x = 6

Answer

x = -3 and x = -6

A rectangular garden has a length that is 5 metres longer than its width.If the area of the garden is 84 m², what is the width of the garden?

A rectangular garden has a length that is 5 metres longer than its width.
If the area of the garden is 84 m², what is the width of the garden?