Question

find the zeros of the polynomial function and state the multiplicity of each.

f(x)=4(x+7)^2(x-7)^3

Answer 1

\(\bf f(x)=4(x+7)^2(x-7)^3\qquad \textit{set the function to 0}\\ \quad \\
0=4(x+7)^2(x-7)^3\implies 0=4{\color{blue}{ (x+7)(x+7)}}{\color{red}{ (x-7)(x-7)(x-7)}}\\ \quad \\
\textit{solve for "x" to get the zeros}\quad multiplicity\quad {\color{blue}{ 2}}\ and \ {\color{red}{ 3}}\)

Answer 2

how is it 2 and 3?

Answer 3

multiplicity = repeats = repetition

Answer 4

I do not believe it is two and three

Answer 5

What number would you multiply by another number to get zero?

Answer 6

anything times zero?

Answer 7

Correct. So we set the function to 0. And we have 0 = 4(x+7)^2 x (x-7)^2 can you look at it and tell how you are going to be able to create a zero in the equation?

Answer 8

x=0?

Answer 9

If x = 0 then it would be 4(0+7)^2 X (0-7) ^ 2 = 9604 not 0. How do you make (x+7) and (x-7) = 0?

Answer 10

x cannot equal 7 or -7

Answer 11

You got it. But they want you to "find the zeros of the polynomial" So the answer is 7 and -7...Great job

Answer 12

thank you!