Question

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

Answer 1

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

Explanation:

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`