how do you factor and how do you find the zeros of:
x^3 - 3x^2
would i need to fill in the missing places, i.e. x^3-3x^2+0x+0 ?
thanks for your help.
2006-09-20 10:29:43 · 7 answers · asked by shih rips 6 in Science & Mathematics ➔ Mathematics
The answers above are correct.
However, your instructor may want you to notice that 0 is a double root.
A cubic polynomial always has 3 roots. Sometimes 2 of them are "imaginary," so there is only one "real" root.
Sometimes all 3 are equal, so there is only one value and it occurs 3 times. (Example: x^3 = 0. The roots are 0, 0, and 0.)
Bottom line: If your teacher is a purist, he/she may want you to show the roots as: 0, 0, 3.
2006-09-20 12:52:09 · answer #1 · answered by actuator 5 · 0⤊ 0⤋
You don't need to find the missing places. Just note that both terms (x^3 and 3x^2) contain x^2 as a factor. Therefore
x^3 - 3x^2 = (x - 3) * x^2
If this is zero, either of the factors is zero, i.e.
x - 3 = 0 OR x^2 = 0, so
x = 3 OR x = 0.
2006-09-20 17:35:26 · answer #2 · answered by dutch_prof 4 · 0⤊ 0⤋
For x^3-3x^2 you first need to factor it:
x^2(x-3)
To find the zeros just set this equal to zero and solve for x:
x^2(x-3)=0; x=0 & 3
2006-09-20 17:44:43 · answer #3 · answered by Rance D 5 · 0⤊ 0⤋
x^3-3x^2=
x^2(x-3)
if you set it equal to zero then
x^2(x-3)=0
x^2=0 so x=0
x-3=0 so x=3
2006-09-20 17:36:14 · answer #4 · answered by Anonymous · 0⤊ 0⤋
x^3 - 3x^2 = x^2(x-3) = 0
that expression will equal zero if either x^2 or (x-3) equals 0.
x = 0 or 3
2006-09-20 17:34:42 · answer #5 · answered by Anonymous · 0⤊ 0⤋
x^3-3x^2 will factor into x^2(x-3)
2006-09-20 17:37:54 · answer #6 · answered by danjlil_43515 4 · 0⤊ 0⤋
factoring this equation is an example of using the greatest common factor. so find the gcf: x^2 then you can get your answer
x^2(x-3)
2006-09-20 17:42:37 · answer #7 · answered by Matty G 2 · 0⤊ 0⤋