42.1k views
4 votes
I am stuck on 20 how do I solve for it?

I am stuck on 20 how do I solve for it?-example-1

1 Answer

4 votes

Given the zeros of the function:


\begin{gathered} 6 \\ 7i \\ -7i \end{gathered}

You can write the equation in Factored Form:


f(x)=\mleft(x-6\mright)\mleft(x-7i\mright)\mleft(x+7i\mright)

Now you need to simplify:

1. Remember this formula:


(a+b)(a-b)=a^2-b^2

In this case:


a=x
b=7i

Therefore, you can rewrite the expression in this form:


f(x)=(x-6)((x)^2-(7i)^2)

2. By definition:


\begin{gathered} i=\sqrt[]{-1} \\ \\ i^2=-1 \end{gathered}

Then:


\begin{gathered} f(x)=(x-6)(x^2-49(-1)) \\ \\ f(x)=(x-6)(x^2+49) \end{gathered}

3. Now you need to use the FOIL Method in order to multiply the binomials. This states that:


(a+b)\mleft(c+d\mright)=ac+ad+bc+bd

Hence:


\begin{gathered} f(x)=(x)(x^2)+(x)(49)-(6)(x^2)-(6)(49) \\ \\ f(x)=x^3+49x-6x^2-294 \end{gathered}

4. Ordering the polynomial from the highest power to the least power, you get:


f(x)=x^3-6x^2+49x-294

Hence, the answer is: Option d.

User Markus Michel
by
7.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories