Question

The polynomial equation x^3-4x^2+2x+10=x^2-5x-3 has complex roots 3+-2i What is the other root? Use a graphing calculator and a system of equations.

A. -3
B. -1
C. 3
D. 10
Please hurry!

Answer 1

B. -1

Explanation:

x^3-4x^2+2x+10=x^2-5x-3

We know it has 3 roots since it is a 3rd degree polynomial.

Two of the roots are (3+2i) and (3-2i)

Subtract x^2-5x-3 from both sides

x^3-4x^2+2x+10-(x^2-5x-3)=x^2-5x-3 -(x^2-5x-3)

Distribute the minus sign

x^3-4x^2+2x+10-x^2+5x+3=x^2-5x-3 -x^2+5x+3

x^3 -5x^2+7x +13 =0

Graphing this equation , we see that it crosses the x axis at x=-1

That covers the three roots, 1 real and two complex