Question

Write a possible polynomial equation with the roots 2,i,-i

Answer 1

To make a polynomial equation with these roots, all we need to do is multiply the following:

(x - 2)(x - i)(x + i)

Now, just use foil and multiply.

(x - 2)x^2 + xi - xi - i^2

(x - 2)x^2 - i^2

i^2 = -1

(x - 2)x^2 + 1

Continue with FOIL.

x^3 + x - 2x^2 - 2

x^3 - 2x^2 + x - 2 is the polynomial expression with the provided roots.

Answer 2

$(x-2)(x-i)(x+i)=(x-2)(x^2+1)=x^3+x-2x^2-2=x^3-2x^2+x-2$