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23 votes
23 votes
What are the zeros of the function y=(x-4)(x² - 12x +36)?

OA. -6, 4, and 6
О в.
O c.
O D. 0, 4, and 6
4 and 6
-6 and -4

User Kevin Brydon
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1 Answer

12 votes
12 votes
To find the zeros, we must completely factor the polynomial:

y=(x-4)(x^2-12x+36) has a quadratic expression in it, which can be factored:

y=(x-4)(x+6)(x+6)

From here, apply the zero product property: if a•b=0, then a=0 or b=0

(0)=(x-4)(x-6)(x-6)

This means, we set each binomial equal to zero, and solve for x:

x-4=0

x=4

x-6=0

x=6

Because the binomial (x+6) accurate twice, it has multiplicity of two, so we only have to write its root once.

The answer is:

x= 4, 6

User Evren Kuzucuoglu
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3.7k points