Question

How to find another zero when given a zero

Answer 1

Ca you be more specific?

Answer 2

if \(a\) is a zero of a polynomial, then \((x-a)\) is a factor of that polynomial

Answer 3

sure

Answer 4

@TuringTest That's correct but I don't think that's what he means.

Answer 5

i need to know how to find another zero with 2 - 3i is a zero of f(x) = x4 - 4x3 + 14x2 - 4x + 13.

Answer 6

oh wait. yeah.

Answer 7

You can use division to factor the rest of the equation,

Answer 8

thnk u

Answer 9

given what TuringTest said

Answer 10

so use syntetic division?

Answer 11

if a+ib is a root, then a-ib is also the root

Answer 12

complex zeroes come in pairs, so if 2 - 3i is a zero, you simply find its pair..

Answer 13

*root or zero

Answer 14

oh ok

Answer 15

To elaborate on hartnn and ganeshie: If the polynomial has real coefficients then complex roots come in conjugate pairs (a+bi and a-bi). Similarly, if the polynomial has rational coefficients, then irrational roots will come in conjugate pairs as well.

Answer 16

thnk u also CliffSedge wish i could give u medal also! =)

Answer 17

u too hartnn

Answer 18

It's ok, I'm sure I'll get plenty more elsewhere *is smug*
In your particular example, if you multiply that complex conjugate pair of factors together, you'll get a quadratic polynomial with real coefficients. You can then factor that out of the original fourth-degree polynomial to yield another quadratic, then it's quadratic formula to find the remaining two roots.
Step four: sit back and admire your work.

Answer 19

haha thnks!

Answer 20

thank u everyone!