Question

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

Answer 1

factor out the gcf x^2

Answer 2

as what @Jim766 said, the problem would be easier to solve. \[\large x^2(x^2-4x+3)=0\] Now concentrate on factoring just the \[\large x^2-4x+3=0\] first. what two numbers add to give -4 but multiply to give +3?

Answer 3

-1 and -3

Answer 4

good :) so we can use -1 and -3 to factor out x^2 -4x+3 \[\large (x^2-4x+3) \implies (x-3)(x-1)=0\] so now you have \[\large x^2=0\]\[\large x-3=0\]\[\large x-1 = 0\] can you solve for all the x's? :)

Answer 5

x = 1 x = 3 and x = 0

Answer 6

good job!! There you go :D

Answer 7

You found the zeroes of the function !

Answer 8

are those the multiplicities too?

Answer 9

mmhmm :)

Answer 10

great. thank you :)

Answer 11

no problem :)

Answer 12

multiplicity refers to their powers