Question

Identify all real roots of the equation: x^4 - 9x^2 + 20 = 0. please show work

Answer 1

We need to factor
use u subsitution
u=x²
we get
u²-9u+20=0
factor
what  2 numbers multiply to get 20 and add to get -9
-4 and -5
(u-4)(u-5)=0
u=x²
(x²-4)(x²-5)=0
factor again
(x-2)(x+2)(x-√5)(x+√5)=0
set equal to zero
x-2=0
x=2
x+2=0
x=-2
x-√5=0
x=√5
x+√5=0
x=-√5


x=-2,-√5,√5,2