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

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

A
$5$
B
$\pm 2$
C
Both 1) and 2)
D
$\pm 3$

Solution:

Given equation:

x^{3} + 5 x^{2} - 4 x - 20

The zeros of

f (x)

are the values of

x

that makes

f (x) = 0

Now,

x^{3} + 5 x^{2} - 4 x - 20 = 0

(x^{3} + 5 x^{2}) + (- 4 x - 20) = 0

x^{2} (x + 5) - 4 (x + 5) = 0

(x^{2} - 4) (x + 5) = 0

Now,

x^{2} - 4 = 0

or

x + 5 = 0

x^{2} = 4

or

x = 5

x = \sqrt{4}

x = \pm 2

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