8.2 Complex Zeros

True or false:

The solution, root, x-intercept, and zero of a problem are all the same thing.

• True

• False, because the solution and root are the same but the x-intercept and zero are opposite signs.

• False, because the x-intercept and root are the same but the zero and solution are opposite signs.

• False, because the x-intercept and solution are the same but the zero and root are opposite signs.

How many real zeros exist for the polynomial?

• 1

• 2

• 3

• 4

Given a zero of a polynomial function, use the Conjugate Root Theorem to find another.

 $7-5i$  

•  $7+5i$  

•  $-7+5i$  

•  $7-5i$  

•  $-7-5i$  

 Write a polynomial function of least degree with the given zeros.

 $x=-2,\ 3+i$ 

•  $f\left(x\right)=x^3-4x^2-2x+20$  

•  $f\left(x\right)=x^3-8x^2+22x-20$  

•  $f\left(x\right)=x^4-6x^3i+6x^2i+24i+40$  

•  $f\left(x\right)=x^4-6x^3+6x^2+24x-40$  

Finish this statement.

 $i^2=$  

• 1

• -1

•  $\pm1$  

•  $\pm\sqrt{-1}$  

Simplify the complex number expression.

 $\left(-3-i\right)\left(6-i\right)$  

•  $-18-3i$  

•  $-18+3i$  

•  $-18-3i-i^2$  

•  $-19-3i$  

 SOLVE:  $x^2=-50$ 
Select the most simplified solution for x.

•  $\sqrt{-50}$  

•  $\pm\sqrt{-50}$  

•  $\pm i\sqrt{50}$  

•  $\pm5i\sqrt{2}$  

Select the correct factored form of a polynomial degree 4, given the complex number solutions of 3i, and 2-5i.

•  $\left(x-3i\right)\left(x-3i\right)\left(x-2-5i\right)\left(x-2-5i\right)$  

•  $\left(x-3i\right)\left(x+3i\right)\left(x-2-5i\right)\left(x+2+5i\right)$  

•  $\left(x-3i\right)\left(x+3i\right)\left(x-2+5i\right)\left(x+2-5i\right)$  

•  $\left(x-3i\right)\left(x+3i\right)\left(x-2+5i\right)\left(x-2-5i\right)$  

Use the given zero of the polynomial to find the remaining zeros.

 $zero:\ 2i$  

 $f\left(x\right)=x^3-4x^2+4x-16$  

•  $zeros:\ -2i,\ +2i$  

•  $zeros:\ +2i,\ +2i$  

•  $zeros:\ -2i,\ +2i,\ 4$  

•  $zeros:\ -2i,\ +2i,\ -4$  

Solve this polynomial function for x.

 $f\left(x\right)\ =\ 2x^2+8$  

Select the simplified correct solutions.

• No solution

• ± 2i

•  $\pm\sqrt{-4}$  

• ± 4i