Question

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

f(x) = 5(x + 6)2(x - 6)3

Answer 1

Is that\[f(x) = 5(x+6)^2(x-6)^3\]?

Answer 2

yes

Answer 3

set y = 0, thus \(\bf f(x) = 5(x + 6)^2(x - 6)^3\implies 0=5(x + 6)^2(x - 6)^3\)

so... what are the zeros?

Answer 4

-6 and 6?

Answer 5

yeap

Answer 6

soo -6 would have multiplicity of 3? and 6 of 2?
wait is 4 a zero too?

Answer 7

the multiplicity it's just \(\bf 0=5(x + 6)^\color{blue}{2}(x - 6)^\color{red}{3}\implies 0=5\color{blue}{(x + 6)(x + 6)}\color{red}{(x - 6)(x - 6)(x - 6)}\)

Answer 8

okay so no 4

Answer 9

yes, the multiplicity, or the times they REPEAT is 2 and 3 respectively

Answer 10

thankyou :)

Answer 11

yw