SOLUTION: The degree three polynomial f(x) with real coefficients and leading coefficient 1, has 4 and 3 + i among its roots. Express f(x) as a product of linear and quadratic polynomials w
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Question 45040This question is from textbook
: The degree three polynomial f(x) with real coefficients and leading coefficient 1, has 4 and 3 + i among its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients.
My answer is f(x)=(x-4)(x^2-6x+9).
Thanks.
This question is from textbook
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
(x - (3 + i))(x - (3 - i))
((x - 3) + i)((x - 3) - i)
(x - 3)^2 + (x - 3)i - (x - 3)i - i^2
x^2 - 6x + 9 - (-1)
x^2 - 6x + 10
then:
(x^2 - 6x + 10)(x - 4) = f(x)
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