SOLUTION: the degree three polynomial f(X) with real coefficients and leading coefficient 1, has 4 and 3+ i among roots. express f(X)as a product of linear and quardratic olynomials with rea

Question 62800: the degree three polynomial f(X) with real coefficients and leading coefficient 1, has 4 and 3+ i among roots. express f(X)as a product of linear and quardratic olynomials with real coefficients.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
the degree three polynomial f(X) with real coefficients and leading coefficient 1, has 4 and 3+ i among roots. express f(X)as a product of linear and quardratic olynomials with real coefficients.
:
The linear polynomial (x - 4)
:
Find the quadratic:
x = 3 + i
x - 3 = i
Square both sides
(x-3)^2 = i^2
x^2 - 6x + 9 = -1
x^2 - 6x + 9 + 1 = 0
x^2 - 6x + 10 = 0
:
mult (x - 4) * (x^2 - 6x + 10) = x^3 - 10x^2 + 34x - 40
:
f(x) = x^3 - 10x^2 + 34x - 40
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