If two of the zeros of the cubic polynomial

Question:

If two of the zeros of the cubic polynomial $a x^{3}+b x^{2}+c x+d$ is 0 , then the third zeros is

(a) $\frac{-b}{a}$

(b) $\frac{b}{a}$

(C) $\frac{c}{a}$

(d) $\frac{-d}{a}$

 

Solution:

(a) $\frac{-b}{a}$

Let $\alpha, 0$ and 0 be the zeroes of $a x^{3}+b x^{2}+c x+d=0$.

Then sum of the zeroes $=\frac{-b}{a}$

$=>\alpha+0+0=\frac{-b}{a}$

$\Rightarrow \alpha=\frac{-b}{a}$

Hence, the third zero is $\frac{-b}{a}$.

 

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