SOLUTION: Please help me with this problem:
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
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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
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Question 54069This question is from textbook Algebra and Trigonometry
: Please help me with this problem:
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. This question is from textbook Algebra and Trigonometry
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 its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients.
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Since the coefficients are real, and since 3+i is a root, 3-1 must be
a root.
so the polynomial has factors: (x-4),(x-(3+i)),(x-(3-i))
f(x) is the product of these three factors.
f(x)= (x-4)((x-3)-i)((x-3)+i)
f(x)= (x-4)((x-3)^2-i^2)
f(x)= (x-4)(x^2-6x+9+1}
f(x)= (x-4)(x^2-6x+10)
f(x)= x^3-10x^2+34x+10
Cheers,
Stan H.
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