and also factor P completely A polynomial P is given Px x3

and also factor P completely

A polynomial P is given. P(x) = x^3 + 5x^2 + 9x (a) Find all zeros of P, real and complex. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)

Solution

a)P(x)=x³+5x²+9x

for zeros

x³+5x²+9x=0

x(x²+5x+9)=0

x=0, (x²+5x+9)=0

(x²+5x+9)=0

x²+5x=-9

x²+5x+(5/2)²=-9+(5/2)²

(x+(5/2))²=-9+(25/4)

(x+(5/2))²=-(11/4)

(x+(5/2))=-(-(11/4)),(x+(5/2))=(-(11/4))

(x+(5/2))=-(i11)/2,(x+(5/2))=(i11)/2

x=-(5/2)-((i11)/2),x=-(5/2)+((i11)/2)

zeros are x=0 ,x=-(5/2)-i((11)/2),x=-(5/2)+i((11)/2)

P(x)=x³+5x²+9x

P(x)=x(x-(-(5/2)-i((11)/2)))(x-(-(5/2)+i((11)/2)))