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[Solved] Equations

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If the inequality ax^2+bx-6<0  has the solution set (x|-2<x<3),  find the values of a and b.

 

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The condition implies that the equation \small ax^2+bx-6=0  has two roots x = -2, x = 3. Vieta's formulas imply 

\small -2+3=-\frac{a}{b}

\small (-2)*3=-\frac{6}{a}

from which we can obtain a = 1, b= - 1.

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