The polynomial equation x3- 4x2 + 2x+ 10 = x2 - 5x-3 has complex roots 3+2i. What is the other root? Use a graphing calculator and a system of equations.

Step-by-step explanation:

Given Equation:

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

which simplifies to

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

Given one of the roots is x = 3x+2i, the conjugate is therefore x = 3-2i.

The product is real, (x-3+2i)(x-3-2i) = x^2-6x+13

The other root can therefore be obtained by long division

(x^3- 5x^2 + 7x+ 13)/(x^2-6x+13) = x+1, or x=-1

Therefore the three roots are:

{x=3-2i, x=3+2i, x=-1 }

just do 5.2 + 2 ( 7.2) and 1/3 x 3 (.9) and youv'e got your equation. 0.9( 9/10) + 7.2 ^2 = 16.4 hope i could !

step-by-step explanation: