Suppose x=3−4i is a zero of the function f(x)=x^4−6x³+29x²−24x+100 . What must be a factor of f ?
Any solutions are greatly appreciated :D
2007-12-13 16:06:30 · 5 answers · asked by nintendogamer91 4 in Science & Mathematics ➔ Mathematics
if 3 - 4i is a zero so is 3 + 4i (conjugate zeros theorem)
if r is a zero of P(x), then x - r is a factor of P(x).
Here we have two zeros, therefore two factors:
x-(3-4i) or x - 3 + 4i
and the second factor: x -(3 + 4i) or x - 3 - 4i
You can find other zeros (factors) but since you are not asking for it I will leave it like this.
good luck
2007-12-13 16:13:43 · answer #1 · answered by Anonymous · 1⤊ 0⤋
1
2007-12-13 16:12:38 · answer #2 · answered by Avia 3 · 0⤊ 1⤋
Imaginary zeros come in pairs, so x=3+4i is also a root. Then a factor is (x-[3+4i])
2007-12-13 16:15:08 · answer #3 · answered by cattbarf 7 · 0⤊ 0⤋
Other roots I found were 2, or -2, 3-4i, 3+4i
Is that what you were looking for?
2007-12-13 16:16:34 · answer #4 · answered by i.heart.u 5 · 1⤊ 0⤋
Complex solutions (ones with i's in them) will always be conjugates (in doubles). so another answer is x=3+4i hoped that helped you :)
2007-12-13 16:10:08 · answer #5 · answered by Duncan B 2 · 1⤊ 0⤋