Write a polynomial in standard form that has the following characteristics. leading coefficient: 3 zeros: -5, 2, 4i

Question

Write a polynomial in standard form that has the following characteristics.

leading coefficient: 3

zeros: -5, 2, 4i

Answer 1

3(x+5)(x-2)(x^2+16) =

3(x^2+3x-6)(x^2+16) =

3(x^4 +3x^3 + 10x^2 +48x -96) =

3x^4 + 9x^3 +30x^2 +144x - 288

Just take each zero and change its sign, then add an x to it to get the factors, then multiply them all together, along with a 3.

(x-4i)(x+4i) = x^2+16. imaginary roots come in conjugate pairs, You can't have one zero without the other.