Find all the zeros of the polynomial Px x3 6x2 6x 5 xSolut

Find all the zeros of the polynomial

P(x) = x³ 6x² + 6x 5

x=

Solution

P(x)=x³-6x²+6x-5

P(x) =(x-5)(x²-x+1)

0=(x-5)(x²-x+1)

x=5 , x²-x+1=0

x=5 , (1+-i sqrt3)/2