Question

Find sum of other zeros of the polynomial $(2x^4-9x^3+5x^2+3x-1)$ if two of its zeros are $(2+\sqrt{3})$ and $(2-\sqrt{3})$.

• A. $\frac{17}{2}$
• B. $\frac{1}{2}$
• C. $\frac{15}{2}$
• D. None of thesse

Answer 1

Answer: (B)

$\frac{1}{2}$

$p\left(x\right)=2x^4-9x^3+5x^2+3x-1$
Let $\alpha =\left(2+\sqrt{3}\right)$, $\beta =\left(2-\sqrt{3}\right)$ and remaining two zeros be $\gamma$ & $\delta$
Now, $\alpha +\beta +\gamma +\delta =-\frac{b}{a}=-\frac{\left(-9\right)}{2}=\frac{9}{2}$
$\Rightarrow 2+\sqrt{3}+2-\sqrt{3}+\gamma +\delta =\frac{9}{2}$
$\Rightarrow 4+\gamma +\delta =\frac{9}{2}$
$\Rightarrow \gamma +\delta =\frac{9}{2}-4$
$\Rightarrow \gamma +\delta =\frac{1}{2}$
Therefore, sum of the other zeros is $\frac{1}{2}$