Px x4 5x2 6 a Find all zeros of P real and complex Enter yo

P(x) = x4 5x2 6
(a) Find all zeros of P, real and complex. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)

x =

(b) Factor P completely.

P(x) =

P(x) = x^4 - 5x^2 -6

substitute x^2 = y

So, we have y^2 - 5y -6

y^2 - 6y +y -6

y(y -6) +1( y -6)

(y+1)(y -6)

y = -1 ; x^2 =-1 ; x = i , -i

y = 6 ; x^2 = 6 ; x = sqrt6 , -sqrt6

So, solution : x = i , -i , sqrt6 , -sqrt6

P(x) = (x +i)(x -i)(x -sqrt6)(x +sqrt6)