SOLUTION: The degree three polynomials f(x) with real coefficients and leading coefficent 1, has 4 and 3+i among its roots. Express f(x) as a product of linear and quadratic polynomials with
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Question 92463This question is from textbook Algebra and Trigonometry
: The degree three polynomials f(x) with real coefficients and leading coefficent 1, has 4 and 3+i among its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients. This question is from textbook Algebra and Trigonometry
You can put this solution on YOUR website! The degree three polynomials f(x) with real coefficients and leading coefficent 1, has 4 and 3+i among its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients.
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Factor when x = 4: (x-4)
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Expression when x = 3 + i:
x - 3 = i; subtracted 3 from both sides
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(x-3)^2 = i^2; squared both sides
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x^2 - 6x + 9 = -1; FOILed (x-3)(x-3), i^2 = -1
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x^2 - 6x + 9 + 1 = 0; added 1 to both sides
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x^2 - 6x + 10 = 0
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Product of a linear and quadratic:
(x-4) * (x^2 - 6x + 10) = (x^3 - 10x^2 + 34x - 40) = f(x)
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