N2012 P2 Q3

Junior College 2

10 marks

It is given that $f(x)=x^3+x^2-2x-4$.

Sketch the graph of $y=f(x)$.[1]
Find the integer solution of the equation $f(x)=4$, and prove algebraically that there are no other real solutions.[3]
State the integer solution of the equation $(x+3)^3+(x+3)^2-2(x+3)-4=4$.[1]
Sketch the graph of $y=|f(x)|$.[1]
Write down two different cubic equations which between them give the roots of the equation $|f(x)|=4$. Hence find all the roots of this equation.[4]

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Answer:(ii) $2$ only. (iii) $-1$. (v) $x^3+x^2-2x-8=0$ or $x^3+x^2-2x=0$; roots $-2,0,1,2$.

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