Question:
If two zeros $x^{3}+x^{2}-5 x-5$ are $\sqrt{5}$ and $-\sqrt{5}$, then its third zero is
(a) 1
(b) $-1$
(c) 2
(d) $-2$
Solution:
Let $\alpha=\sqrt{5}$ and $\beta=-\sqrt{5}$ be the given zeros and $\gamma$ be the third zero of $x^{3}+x^{2}-5 x-5=0$ then
By using $\alpha+\beta+\gamma=\frac{-\text { Coefficient of } x^{2}}{\text { Coefficient of } x^{3}}$
$\alpha+\beta+\gamma=\frac{+(+1)}{1}$
$\alpha+\beta+\gamma=-1$
By substituting $\alpha=\sqrt{5}$ and $\beta=-\sqrt{5}$ in $\alpha+\beta+\gamma=-1$
$\gamma=-1$
Hence, the correct choice is (b)
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