How do you find all the zeros of f(x)=x^4-5x^2-36f(x)=x4−5x2−36?

1 Answer
Bdub
Mar 10, 2016

x={-3,-2,2,3}x={−3,−2,2,3}

Explanation:

let u=x^2u=x2 then f(x)=x^4-5x^2-36 ->f(u)=u^2-5u-36f(x)=x4−5x2−36→f(u)=u2−5u−36
u^2-5u-36=0u2−5u−36=0
(u-9)(u+4)=0(u−9)(u+4)=0
u-9=0,u+4=0u−9=0,u+4=0
u=9 or u=-4u=9oru=−4
x^2=9,x^2=4x2=9,x2=4
x=+-3,x=+-2x=±3,x=±2
x={-3,-2,2,3}x={−3,−2,2,3}

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