Solve x2 +2x – 4 = 0, leaving your answer in simplest surd form (4 marks, non calculator question)

'Simplest surd form' is a clue that quadratic factorising will not work for this question, so we must instead use the quadratic formula. It is always a good idea to quote this as marks are often available for quoting formulae.

x = [-b±√(b^2-4ac)]/2a  where ax^2 + bx + c = 0

Thus, a = 1, b = 2, c = -4

Sub this data into the formula:

[-2 ± √2^2 - (4 x 1 x -4)] / (2x1)

This question is non-calculator, so simplify down to get

[-2 ± √(4 + 16)] / 2

[-2 ± √20 ] / 2

√20 can be simplified (important as the question states in simplest surd form)

√20  = √5√4 = 2√5

[-2 ± 2√ 5] / 2

Thus x = -1 ± √5