Question

Find all the zeros of the polynomial 2x^3+x^2-6x-3.if two of its zeros are root 3 and -root 3

Answer 1

i hope this will usful to u

Answer 2

The zeroes of given polynomial $\bold{-\frac{1}{2}}$.

To find:

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

Solution:

Given: $2 x^{3}+x^{2}-6 x-3$  

Since $x=\sqrt{3}\ is\ a\ zero,\ x-\sqrt{3}$ is a factor  

$\&\ x=-\sqrt{3}$ is a zero, $x+\sqrt{3}$ is a factor  

Hence $(x+\sqrt{3})(x-\sqrt{3})$ is also a factor  

$\begin{array}{l}{=\left(x^{2}-(\sqrt{3})^{2}\right.} \\ \\ {=\left(x^{2}-3\right)}\end{array}$

Now for other zero, we divide the polynomial by $\left(x^{2}-3\right)$  

Therefore, $2 x^{3}+x^{2}-6 x-3=\left(x^{2}-3\right)(2 x+1)$

Hence, $\left(x^{2}-3\right)(2 x+1)=0$

i.e., $x=-\frac{1}{2}$

Therefore, the zeroes of given ‘polynomial’ are $-\frac{1}{2}, \sqrt{3},-\sqrt{3}$.