A graphing calculator is not to be used in answering this question. One root of the equation ${{x}^{

Question

A graphing calculator is not to be used in answering this question.

One root of the equation ${{x}^{4}}+a{{x}^{3}}+5{{x}^{2}}-x-10=0$, where $a$ is real, is$x=1+2\mathrm{i}$. Find the value of $a$ and the other roots.[5]

Hence find the $x$-coordinates of the point(s) of intersection between the graphs of $y=5\left( {{x}^{2}}-2{{x}^{4}} \right)$ and $y={{x}^{3}}+3x-1$.[3]

Accepted Answer

$a=-3$, with other roots $x=2,-1,1-2\mathbf{i}$ The intersection $x$-coordinates are $x=-1,\dfrac12$

2013 MJC P2 Q1

2013 MJC P2 Q1

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