x^4-25x^2+60x-36=0

Question

x^4-25x^2+60x-36=0

Answer 1

X³(x-2)+2x²(x-2)-21x(x-2)+18(x-2)=0
(x-2)(x³+2x²-21x+18)=0
(x-2)[x²(x-1)+3x(x-1)-18(x-1)]=0
(x-2)(x-1)(x²+3x-18)=0
(x-2)(x-1)[x(x-3)+6(x-3)]=0
(x-2)(x-1)(x-3)(x+6)=0
x-2=0⇒x=2
x-1=0⇒x=1
x-3=0⇒x=3
x+6=0⇒x=-6