It is given that $\mathrm{f}(x)=3x^3+2x^2+16$. The remainder when $\mathrm{f}(x)$ is divided by

Question

It is given that $\mathrm{f}(x)=3x^3+2x^2+16$. The remainder when $\mathrm{f}(x)$ is divided by $x-3a$, where $a$ is a constant is the same as the remainder when it is divided by $3x+2$. Find the possible values of $a$.[3] Show with clear working, that $x=-2$ is a solution of $\mathrm{f}(x)=0$.[2] Explain why $\mathrm{f}(x)=0$ has only one real root.[5] Hence use your answers to parts (b) and (c) to solve the equation $$16y^3+2y-3=0$$[2]

Accepted Answer

(a) $a=0$ or $a=-\frac{2}{9}$ (b) $x=-2$ (c) Only one real root (d) $y=\frac{1}{2}$

Quadratic Functions, Equations and Inequalities - Nature of Roots of Quadratic Equations

Quadratic Functions, Equations and Inequalities - Nature of Roots of Quadratic Equations

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