GCSE Solving Quadratic Equations 3

Question 1

Solve x² = 49.

Accepted Answer

x = ±7

Answer

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?

Accepted Answer

Difference of two squares

Answer

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?

Accepted Answer

8

Answer

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.

Accepted Answer

x = 5 and x = −2

Answer

x = (3 ± √49) / 2 = (3 ± 7) / 2, giving x = 5 or x = −2.

Question 5

Solve 4x² − 1 = 0.

Accepted Answer

x = ±½

Answer

4x² = 1, x² = ¼, so x = ±½.

GCSE - General Certificate of Secondary Education Practice Test