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If the polynomial x^2+bx+c has exactly one real root and b=c+7, find the value of the product of all possible values of c.

 Dec 21, 2021
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If a quadratic has one root, it must be a perfect square. Let's say the polynomial factors as (x+m)^2. Then, b = 2m and c = m^2. If 2m = m^2 + 7, m^2-2m+7=0. By vieta's formulas, the product of the solutions is 7. Thus, we square this to get 49.

(as a note, there are imaginary values for b and c, which I'm unsure are allowed here)

See https://web2.0calc.com/questions/need-the-answer-quick for more information. 

 Dec 21, 2021
edited by tinfoilhat  Dec 21, 2021

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