Find the polynomial p(x)

Question

P(x) is a 3rd degree polynomial with zeros 3 and 2i

Answer 1

3 and 2i are zeros

x=3

x-3=0

x-3 is a factor

x=2i

square both sides

x^2=(2i)^2 = 4(-1)

x^2 = -4

x^2 +4 =0

x^2+4 is another factor

multiply the two factors together

p(x) = (x-3)(x^2 +4)

p(x) = x^3 -3x^2 + 4x -12

check the answer, plug in x=3

3^3 -3(3^2) +4(3) -12

=27-27+12-12

=0

plug in x=2i

(2i)^3 -3(2i)^2+4(2i) -12

=-8i +12 -8i +12

= 0

you could also have

p(x) = ax^3 -3ax^2 +4ax -12 as a 3rd degree polynomial

where a = any integer or real number. they also has 3 and 2i as zeros

-2i is a 3rd zero since imaginary zeros always come in conjugate pairs

inseparable, like lovebirds