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

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) (Show Source): You can put this solution on YOUR website!
The equation would have the form,

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,

So then,

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