The polynomial equation x3- 4x2 + 2x+ 10 = x2 - 5x-3 has complex roots 3+2i. What is the other root? Use a graphing
1 answer:
Answer:
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 }
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