Find all the zeros of f(x)=x3+5×2-4x-20?

# Find all the zeros of $f\left(x\right)={x}^{3}+5{x}^{2}-4x-20$?

1. A
$5$
2. B
$±2$
3. C
Both 1) and 2)
4. D
$±3$

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### Solution:

Given equation: ${x}^{3}+5{x}^{2}-4x-20$
The zeros of $f\left(x\right)$ are the values of $x$ that makes $f\left(x\right)=0$
Now,
${x}^{3}+5{x}^{2}-4x-20=0$
$\left({x}^{3}+5{x}^{2}\right)+\left(-4x-20\right)=0$
${x}^{2}\left(x+5\right)-4\left(x+5\right)=0$
$\left({x}^{2}-4\right)\left(x+5\right)=0$
Now,
${x}^{2}-4=0$                 or               $x+5=0$
${x}^{2}=4$                         or              $x=5$
$x=\sqrt{4}$
$x=±2$

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