79.0k views
4 votes
find all other zeros of p (x)= x^3-x^2+8x+10, given that 1+3i is a zero. ( if there is more than one zero, separate them with commas.)edit: if possible please double check answers would high appreciate it.

find all other zeros of p (x)= x^3-x^2+8x+10, given that 1+3i is a zero. ( if there-example-1
User Frbl
by
7.8k points

1 Answer

4 votes

Since we have that 1 + 3i is one zero of p(x), then we have that its conjugate is also a root, then, we have the following complex roots for p(x):


\begin{gathered} x=1-3i \\ x=1+3i \end{gathered}

also, notice that if we evaluate -1 on p(x), we get:


\begin{gathered} p(-1)=(-1)^3-(-1)^2+8(-1)+10=-1-1-8+10 \\ =-10+10=0 \end{gathered}

therefore, the zeros of p(x) are:

x = 1-3i

x = 1+3i

x = -1

User Scott Gigante
by
7.5k 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