How do you find all the zeros of $F(x) = 9x^4 - 37x^2 + 4$ ?

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Answer 1 · 2016-02-28T14:28:31

The zeroes are $1/3,-1/3,2,-2$

We notice that

$F(x)=9x^4-37x^2+4=9x^4-36x^2+4-x^2= 9x^2(x^2-4)-(x^2-4)=(9x^2-1)(x^2-4)= (3x-1)*(3x+1)(x+2)(x-2)$

Hence the zeroes are the values for which

$F(x)=0=>(3x-1)(3x+1)(x+2)(x-2)=0$

which are $x_1=1/3,x_2=-1/3,x_3=2,x_4=-2$

How do you find all the zeros of F(x) = 9x^4 - 37x^2 + 4F(x) = 9x^4 - 37x^2 + 4?