SOLUTION: the degree 3 polynomial f(x) with real coefficients and leading coefficents 1, has 4 and 3+i among its roots. express f(x) as a product of linear and quadratic polynomials with rea
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Question 56810This question is from textbook
: the degree 3 polynomial f(x) with real coefficients and leading coefficents 1, has 4 and 3+i among its roots. express f(x) as a product of linear and quadratic polynomials with real coefficents. This question is from textbook
You can put this solution on YOUR website! the degree 3 polynomial f(x) with real coefficients and leading coefficents 1, has 4 and 3+i among its roots. express f(x) as a product of linear and quadratic polynomials with real coefficents.
:
Let (x-4) be one factor:
:
Find x = 3 + i
x - 3 = i
Square both sides:
(x-3)^2 = i^2
:
FOIL (x-3)^2 and i^2 = -1
x^2 - 6x + 9 = -1
:
x^2 - 6x + 9 + 1 = 0
:
x^2 - 6x + 10 = 0 is the quadratic polynomial
:
Mult by the other factor (x-4)
(x-4)*(x^2 - 6x + 10) = x^3 - 10x^2 + 34x - 40, a 3rd degree polynomial
