SOLUTION: Find a polynomial with the given zeros. 1, -1, square root of 2, negative square root of 2

Question 167736: Find a polynomial with the given zeros.
1, -1, square root of 2, negative square root of 2
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Since , , , and are given zeros this means that:

, , , and

Squaring both sides of the last two equations gets: and

So we really have 3 equations , , and

Get all terms to the left side in each case

, , and

Now use the zero product property in reverse to join the factors.

FOIL to get

FOIL

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Answer:

So the polynomial with roots of , , , and is

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