Help please

K

kaebun

Junior Member
Joined
Sep 11, 2005
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135
using given zero, find all of the zeros and write a linear factorization of f(x)
1+i is a zero of f(x)=x^4-2x^3-x^2+6x-6
i know that another zero is 1-i but thats about as far as i got
 
If, say, x = 3 were a zero, then x - 3 would be a factor.

If, in this case, x = 1 + i is a zero, then what is a factor?

Since complex roots come in conjugate pairs, what else must necessarily be a zero? So what else is a factor?

Multiply these two factors together. Then divide this quadratic out of the fourth-degree polynomial. Apply the Quadratic Formula to the result to find the other two roots.

Eliz.
 
Maybe you can do it like this.

You know that

x = 1 (+/-)sqrt(-1)

Working 'backwards' to find the factor

x - 1 = (+/-)sqrt(-1)

(x - 1)^2 = -1

(x - 1)^2 + 1 =

x^2 -2x+2, is a factor

Using long division

..................x^2 - 3
.................__________________
x^2 -2x+2 |x^4-2x^3-...x^2+6x-6
..................x^4-2x^3+2x^2
..................______________
..................................-3x^2+6x-6
..................................-3x^2+6x-6
..................................__________
..................................................0

Find the other zeros.

x^2 - 3= 0

Solve for x

x = (+/-)sqrt(3)

What's the linear factorization?
 
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