Create px given the following zeros x3 x 15i x0SolutionZeroz

Create p(x) given the following zeros:

x=-3

x= -1+5i

x=0

Solution

Zeroz are : x = -3

x= -1 +5i another root would be conjugate of -1 +5i = -1 -5i

x = 0

So, p(x) = x(x+3)(x+1 -5i)(x+1 +5i)

= x(x+3)(x^2 +5ix + x + x +1+5i -5ix -5i +25)

= x(x+3)(x^2 +2x +26)

p(x) = x(x+3)(x^2 +2x +26)