Form a polynomial(x) with real coefficients having the given degree and zeros.

Question

Degree; 5 zeros:-4; -i; -2+i

Answer 1

zeros are -4, -i and -i+1

x=-4

x+4 =0

x +4 is a factor

imaginary zeros come in conjugate pairs

so if -i is a zero so is +i

if -i+1 is a zero so is +i+1

x=-i= (-1)(i)

x^2 = (-1)^2(i)^2 = 1(-1) = -1

x^2 = -1

x^2 +1 = 0

x^2 + 1 is another factor

x= -2+i

x+2 = i

x^2 +4x +4 =-1

x^2 +4x +5 = 0

x^2 +4x +5 is another factor

multiply the factors together

(x+4)(x^2+1)(x^2-4x+5)

= x^5 + 8x^4 -10x^3 + 20x^2 - 11x + 20

Answer 2

P(x) = (x - (-4))(x - (-i))(x - (i))(x - (i - 2))(x - (i + 2)).

Each factor is x minus the "zero".