Question

HELP PLEASE
Find the zeros of f(x)=(x+5)^5(x-3)^6 and state the multiplicity.

Answer 1

to find the zeros you need to solve

x + 5 = 0 and x - 3 = 0

the multiplicity of each zero will be the power of the factor

(x + 5)^5 has multiplicity of 5... I'll let you work out the multiplicity of the other factor.

hope it helps

Answer 2

Set the function equal to zero:
(x + 5)^5(x - 3)^6 = 0
Because of the exponent of 5 on x + 5, you have 5 of those factors:
(x + 5)(x + 5)... 5 equal factors
Because of the exponent of 6 on x - 3, you have 6 of those factors
(x - 3)(x - 3) ... 6 equal factors
Solve (x + 5)(x - 3) = 0
x + 5 = 0 or x - 3 = 0
x = -5 or x = 3
Because the x + 5 has a 5 exponent, the multiplicity is 5
Because the x - 3 has an exponent of 6, the multiplicity is 6
So the answer is x = -5 multiplicity 5 or x = 3 multiplicity 6

Answer 3

the other has a multiplicity of 6? so answer would be???

Answer 4

THANKS!

Answer 5

thats correct... you just need to find the roots... by solving the equations...

x + 5 = 0

and x - 3 = 0