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.

The roots of the polynomial equation are:

-1,3+2i and 3-2i

Step-by-step explanation:

We are given a polynomial equation as:

this equation could also be written as:

and

Now if this equation has a complex root as:

and we know that for any polynomial equation witth real coefficients the complex roots always appear in pair.

if a+ib is some root of a polynomial equation with real coefficients then its conjugate a-ib is also a root of the equation.

Hence, the other root of this polynomial equation will be:

Now we will graph these system of equations i.e. equation (1) and equation (2).

on solving the equation we have:

(since

)

Hence on solving the equation we have:

x=-1,3+2i and 3-2i are the roots of the equation.

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step-by-step explanation: