Question 0118

Equations and Inequalities

2018 Paper 1 Question 4 Variant

Question

(i)

Find the exact roots of the equation

|2 x^2 - 2 x - 5| = 5 - 2 x

[4]

(ii)

On the same axes, sketch the curves with equations

{y=|2 x^2 - 2 x - 5|}

and

{y=5 - 2 x.}

Hence solve the inequality

|2 x^2 - 2 x - 5| < 5 - 2 x.

[4]