Question

Find all the zeros of the polynomial $2x^3+x^2-6x-3$, if two of its zeros are $-\sqrt{3}$ and $\sqrt{3}$

• A. Third zero $=-\frac{1}{2}$
• B. Third zero $=\frac{1}{2}$
• C. Third zero $=-\frac{3}{2}$
• D. Third zero $=\frac{3}{2}$

Answer 1

The correct option is A Third zero $=-\frac{1}{2}$

Let $f\left(x\right)=2x^3+x^2-6x-3$
The zeros are $-\sqrt{3}$ and $\sqrt{3}$
Let the other zero be $\alpha$
$=\alpha (-\sqrt{3})\left(\sqrt{3}\right)=-\frac{(-3)}{2}$

$=>-3\alpha =\frac{3}{2}$

$=>\alpha =\frac{-1}{2}$