If the roots of {x^2} + x + a = 0exceed a, th | vedclass

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(d) If the roots of the quadratic equation $a{x^2} + bx + c = 0$ exceed a number k, then $a{k^2} + bk + c > 0$ if $a > 0,$ ${b^2} - 4ac \ge 0$ a

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$a < - 2$

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(d) If the roots of the quadratic equation $a{x^2} + bx + c = 0$ exceed a number k, then $a{k^2} + bk + c > 0$ if $a > 0,$ ${b^2} - 4ac \ge 0$ and sum of the roots $ > 2k$ Therefore, if the roots of ${x^2} + x + a = 0$ exceed a number a, then ${a^2} + a + a > 0,1 - 4a \ge 0$ and $ - 1 > 2a$ ==> $a(a + 2) > 0,$$a \le \frac{1}{4}$and $a < - \frac{1}{2}$ ==> $a > 0\,{\rm{or}}\,a < - 2,a < \frac{1}{4}$and $a < - \frac{1}{2}$ Hence $a < - 2$.

If the roots of ${x^2} + x + a = 0$exceed $a$, then

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