How do you find all the zeros of $-5x^2(x-9)(x+4)^3$ ?

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Answer 1 · 2018-06-30T22:52:28

$x=0, 9$ and $-4$ .

Let's set all terms equal to zero:

$color(blue)(-5x^2=0)$

We need to take the square root of both sides to get

$-5x=0$

$color(blue)(x=0)$

$color(purple)(x-9=0=>x=9)$

$(x+4)^3=0$

In this case, we need to take the cube root of both sides. We get

$color(red)(x+4=0=>x=-4)$

Therefore, the zeroes are at

$x=0, 9$ and $-4$ .

Hope this helps!

How do you find all the zeros of -5x^2(x-9)(x+4)^3-5x^2(x-9)(x+4)^3?