SOLUTION: Write a polynomial function f(x), in standard form, of the least degree that has real coefficients, the given zeros (3, -4, 2+[square root of 5]), and a leading coefficient of 1.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Write a polynomial function f(x), in standard form, of the least degree that has real coefficients, the given zeros (3, -4, 2+[square root of 5]), and a leading coefficient of 1.       Log On


   



Question 676344: Write a polynomial function f(x), in standard form, of the least degree that has real coefficients, the given zeros (3, -4, 2+[square root of 5]), and a leading coefficient of 1.
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
x = 3, so x-3 = 0
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x = -4, so x+4=0
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x = 2%2Bsqrt%285%29, so x - 2 = sqrt%285%29; therefore, %28x-2%29%5E2=5, so %28x-2%29%5E2+-+5+=+0
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%28x-3%29%28x%2B4%29%28x-2%29%5E2-5+=+0
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Foil (x-3)(x+4)
Foil (x-2)(x-2)
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%28x%5E2%2B4x-3x-12%29%28x%5E2-4x%2B4%29-5=0
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%28x%5E2%2Bx-12%29%28x%5E2-4x%2B4%29-5=0
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x%5E4+-+4x%5E3+%2B+4x%5E2+%2B+x%5E3+-+4x%5E2+%2B+4x+-+12x%5E2+%2B+48x+-+48+-+5+=0
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highlight_green%28x%5E4+-+3x%5E3+-+12x%5E2+%2B+52x+-+53=0%29
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