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If-the-roots-of-quadratic-equation-ax-2-bx-c-0-were-within-the-interval-0-1-the-maximum-value-from-2a-b-a-b-a-a-b-c-is-




Question Number 10168 by Joel575 last updated on 28/Jan/17
If the roots of quadratic equation  ax^2  + bx + c = 0  were within the interval [0,1],  the maximum value from  (((2a−b)(a−b))/(a(a−b+c)))    is ...
$$\mathrm{If}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{quadratic}\:\mathrm{equation} \\ $$$${ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:=\:\mathrm{0} \\ $$$$\mathrm{were}\:\mathrm{within}\:\mathrm{the}\:\mathrm{interval}\:\left[\mathrm{0},\mathrm{1}\right], \\ $$$$\mathrm{the}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{from} \\ $$$$\frac{\left(\mathrm{2}{a}−{b}\right)\left({a}−{b}\right)}{{a}\left({a}−{b}+{c}\right)}\:\:\:\:\mathrm{is}\:… \\ $$

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