SOLUTION: find all of the rational zeros of this function f(x) = x^4 - 49x^2

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Question 282094: find all of the rational zeros of this function f(x) = x^4 - 49x^2
Answer by nabla(475) About Me  (Show Source):
You can put this solution on YOUR website!
Rewrite as:
%28x%5E2%29%5E2-%287x%29%5E2=0
Use difference of squares formula.
%28x%5E2%2B7x%29%28x%5E2-7x%29=0
So we want:
x^2+7x=0 or x^2-7x=0
ie:
x(x+7)=0 or x(x-7)=0
x=-7 or 0; or x=7 or 0

Hence we have solution set {-7,0,7} with 0 occurring twice.