Question

Find an nth-degree polynomial function with real coefficients satisfying the given conditin=3;3 and 5 i are zeros;f(1) = -52

Answer 1

Given:

3 and 5i are the roots of the equation.

It is given that n=3 .

Let assume the third root be the conjugate of complex root that is -5i

Then the polynomial function :

`f(x)=(x-3)(x-5i)(x+5i)`
`f(x)=(x-3)(x^2+25)`
`f(x)=x^3+25x-3x^2-75`
`f(x)=x^3-3x^2+25x-75`
`\text{The polynomial function be }f(x)=x^3-3x^2+25x-75`

Given that f(1)= -52,

`f(1)=1-3+25-75`
`f(1)=-52`