Question

find all the zeros of f(x)=x^3-3x^2+4x-12

Answer 1

set f(x) = 0, and what factor of x^3 - 3x^2 ?
what factor of 4x - 12 ?
can you factor those ?

Answer 2

@tamtoan the zero is -12 are there any other zeros that I don't see. What do I do with the factor of (x^3-3x^2) and (4x-12).

Answer 3

factor them, and then group them, and set those 2 factors equal zero, then you will find the solution...can you tell me the factors?

Answer 4

find all zeros in a function means ..that you have to set that function equal to zero ...ie...find all value of x such that f(x) = 0

Answer 5

the factors are x^2(x-3) and 4(x-3) so I set them both to 0 and find the solution

Answer 6

ok now , x^3-3x^2+4x-12 = 0

so you have x^2(x-3) + 4(x-3) = 0

can you do one more step factoring from here and let me know?

Answer 7

no

Answer 8

look at both of the terms, what do they have in common?

Answer 9

x-3

Answer 10

ok if x-3 is the common term, then you can factor that out, correct? ...can you show me how you factor that?

Answer 11

nope i dont know how to factor out

Answer 12

ok...let me do this for you, if anything you don't understand, ask a question again ok?

find all the zeros of f(x)=x^3-3x^2+4x-12

set f(x) = 0, then x^3-3x^2+4x-12 = 0
x^2(x-3) + 4(x-3) = 0

since both terms have x-3, factor that out, you have:

(x-3)(x^2 + 4) = 0

now 2 factors multiple each other equal to zero means either one of them is zero.

so you will have : x - 3 = 0 or,
x^2 + 4 = 0

the first one, you can solve easy right?

the second one, if you already learn complex number, you can solve that too, let me know your answer ?

Answer 13

thanks

Answer 14

you got it right? , can you please tell me what are the zeros ? ie. value of x ?