Question

If two zeroes of the polynomial $x^4+3x^3-20x^2-6x+36$ are $\sqrt{2}$ and -$\sqrt{2}$, find the other zeroes of the polynomial

Answer 1

$x^4+3x^3-20x^2-6x+36$

Two zeroes are $\sqrt{2},-\sqrt{2}$

$\therefore (x-\sqrt{2})(x+\sqrt{2})$ are the factors of the polynomial

$\Rightarrow x^2-2$ is a factor

$\therefore$ Quotient $=x^2+3x-18$

To find other two factors

$x^2+3x-18=0\Rightarrow x^2+6x-3x-18$

$\Rightarrow x(x+6)-3(x-6)$

$\Rightarrow (x+3)(x+6)=0$

$\Rightarrow x=3\&-6$