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Suppose that a and b  are nonzero real numbers, and that the equation \(x^2+ax+b=0\) has solutions a and b. Find the ordered pair (a,b).

 Dec 25, 2018
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\(\text{as }a \text{ and }b \text{ are solutions to }x^2 + ax + b = 0\\ \text{we can write}\\ x^2 + ax + b = (x-a)(x-b) = x^2 -(a+b)x + ab\\ a = -(a+b) \text{ and } b= a b\\ b = -2a\\ b = a(-2a) = -2a^2\\ -2a = -2a^2 \Rightarrow a = 1\\ b = -2a = -2\\ (a,b) = (1,-2) \)

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 Dec 25, 2018

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