Solve the equation $x^2-6x+34=0$.[2] One root of the equation $x^4+4x^3+x^2+ax+b=0$, where

Question

Solve the equation $x^2-6x+34=0$.[2] One root of the equation $x^4+4x^3+x^2+ax+b=0$, where $a$ and $b$ are real, is $x=-2+\mathrm i$. Find the values of $a$ and $b$ and the other roots.[5]

Accepted Answer

(i) $3\pm5\mathrm i$. (ii) $a=-16,b=-20$; other roots $-2-\mathrm i,2,-2$.

N2010 P2 Q1

N2010 P2 Q1

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