Question

Homework: Section 3.4HomeworkQuestion 6, 3.4.25 >HW Score: 50%, 5 of 10 pointsO Points: 0 of 1SaveFind an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verifythe real zeros and the given function value.n=3;3 and 4 i are zeros;f(2)=40f(x)=(Type an expression using x as the variable. Simplify your answer.)Clear allCheck answerHelp me solve thisView an example Get more help.

Answer 1

The roots are

$\begin{gathered} x=3 \\ x=4i \\ x=-4i \end{gathered}$

The polynomial can be modellled as ;

$f(x)=a(x-3)(x-4i)(x+4i)$

$f(x)=a(x-3)(x^2+16)$

Let us use f(2) to obtain a value for a

$\begin{gathered} f(2)=a(2-3)(2^2+16) \\ 40=-20a \\ a=-2 \end{gathered}$

The polynomal f(x) is given as

$\begin{gathered} f(x)=-2(x-3)(x^2+16) \\ f(x)=-2x^3+6x^2-32x+96 \end{gathered}$