Question

Build a polynomial function having real coefficients with degree = 3 and zeros x = -7 and x = 3i. Write your answer in the form f (x) = ax3 + bx2 + cx + d . (8 pts.)

Answer 1

∴f(x)
`=x^3-7x^2+9x-63`

Explanation:

Given that, a polynomial of real coefficient with degree 3.

x= -7 and x= -3i are two zeros of the given polynomial.

Conjugate Root Theorem:

The conjugate root theorem state that, if the complex number a+bi is a zero of a polynomial f(x) with real coefficient in one variable, then the complex conjugate a-bi is also a zero of that polynomial.

∴f(x)

= {x-(-7)}(x-3i){x-(-3i)}

=(x-7)(x-3i)(x+3i)

=(x-7){x²-(3i)²}

=(x-7)(x²-9i²)

=(x-7)(x²+9)

`=x^3-7x^2+9x-63`

∴f(x)
`=x^3-7x^2+9x-63`