Question

For each of the following, find a polynomial function of the lowest degree with rational coefficients that have the given numbers as some of its zeros. a) zeros -5 and 2b) zeros 4, and -3i

Answer 1

`f(x)=x^(2)+3x-10`

Explanations:

The standard equation of a polynomial as a function of "x" is expressed as:

`f(x)=(x-a)(x-b)...(x-n)`

where a, b and n are the zero's of the polynomial.

Given the following zeros -5 and 2, the required polynomial will be expressed as:

`\begin{gathered} f(x)=(x-(-5))(x-2) \\ f(x)=(x+5)(x-2) \end{gathered}`

Expand

`\begin{gathered} f(x)=x(x)-2x+5x-5(2) \\ f(x)=x^2+3x-10 \end{gathered}`