Question

Obtain other zeros of the polynomial $f(x)=2 x^4+3 x^3- 5 x^2$ $-9 x-3$ if two of its zeroes are $\sqrt{3}$ and $-\sqrt{3}$.

Answer 1

Since $\sqrt{3}$ and $-\sqrt{3}$ are zeroes of $f(x),(x-\sqrt{3})(x+\sqrt{3})$

i.e., $\left(x^2-3\right)$ is a factor of $f(x)$ to obtain other two zeroes, we shall determine the quotient, by dividing $f(x)$ with $\left(x^2-3\right)$.

Here, quotient $=2 x^2+3 x+1$

$=(2 x+1)(x+1)$

So, The two zeroes are $-1$ and $-\frac{1}{2}$.