SOLUTION: Suppose that a polynomial function of degree 4 with rational coefficients has 6, 4, and sqrt2 as zeros. Find the other zero

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Suppose that a polynomial function of degree 4 with rational coefficients has 6, 4, and sqrt2 as zeros. Find the other zero      Log On


   

Question 882934: Suppose that a polynomial function of degree 4 with rational coefficients has 6, 4, and sqrt2 as zeros.
Find the other zero
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The equation would have the form,
f%28x%29=a%28x-6%29%28x-4%29%28x-sqrt%282%29%29%28x-b%29
Since the coefficients are rational, then,
The product of the last two factors must cancel out the x term to eliminate the irrational coefficient.
That can be done by having a difference of squares since,
%28x-c%29%28x%2Bc%29=x%5E2-c%5E2
So then,
highlight%28b=-sqrt%282%29%29
%28x-sqrt%282%29%29%28x%2Bsqrt%282%29%29=x%5E2-2