Question

What are the zeroes of the function? What are their multiplicities?
f(x) = x^4 - 4x^3 + 3x^2

A. The number -1 and -3 are zeroes of multiplicity 2; the number 0 is a zero of multiplicity 1.
B. The number 0 is a zero of multiplicity 2; the numbers 1 and 3 are zeroes of multiplicity 1.
C. The numbers 0 and 1 are zeroes of multiplicity 2; the number 3 is a zero of multiplicity 1.
D. The number 0 is a zero of multiplicity 2; the numbers -1 and -3 are zeroes of multiplicity 1.

Fan and medal will be given to whomever can offer the most help :) thank you in advance!

Answer 1

Something's missing from your f(x) = x^4 - 4^3 + 3x^2 Please check it and fix it. Thx

Answer 2

Fixed! Sorry @mathmale

Answer 3

take x^2 common then x^2(x^2-4x+3)

Answer 4

Please explain why you're doing this, Er_M.

Answer 5

fine

Answer 6

Wait, one of the parts you posted got deleted

Answer 7

now factor it

Answer 8

i delete it since COC

Answer 9

but most of user not think about COC @mathmale

Answer 10

x^2 = 0 ---> x = 0 (multiplicity of 2)

Answer 11

@Ray1998 try to make factor of +3 as its multiplication is 3 and sum is 4

Answer 12

yes

Answer 13

That's the answer?

Answer 14

no not complete answer

Answer 15

x*x(x*x-4x+3) solve x*x-4x+3 for other zeros

Answer 16

The zeros are 0 (mult. 2), 3 (mult. 1), and 1 (mult. 1) correct?

Answer 17

yes

Answer 18

Yay! Thank you for all your help ^.^ @Er.Mohd.AMIR