Question

Find the zeros of the polynomial function and state the multiplicity of each.
f(x) = 3(x + 7)^2(x - 7)^3

Answer 1

I think the zeros are -7 and 7...whats the multiplicity?

Answer 2

Yes, the equation is only ever equal to 0 when either x is -7 or x is 7. Thus:

Zeros: x = -7, 7

Multiplicities are just the number of times each zero occurs. That is to say, the power or exponent of the zero.

In this case, we (x+7)^2 and (x-7)^2, each occurs twice. Therefore, the multiplicity of the zero x = -7, is 2 (since it's power is 2), and the multiplicity of the zero x = 7 is also 2 (since it's power is also 2).

Answer 3

thanks so much I understand now!

Answer 4

oh wait, my choices have:

-7, multiplicity 2; 7, multiplicity 3

-7, multiplicity 3; 7, multiplicity 2

Answer 5

+7 must be 3 correct?
so option 1?

Answer 6

thanks :)