Question 0118

Equations and Inequalities
2018 Paper 1 Question 4 Variant

Question

(i)
Find the exact roots of the equation
x23x2=2+x|x^2 - 3 x - 2| = 2 + x
[4]
(ii)
On the same axes, sketch the curves with equations y=x23x2{y=|x^2 - 3 x - 2|} and y=2+x.{y=2 + x.}
Hence solve the inequality
x23x2>2+x.|x^2 - 3 x - 2| > 2 + x.
[4]

Answer