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!