Solving a quadratic Inequality Solve 9x−14−x2&gt;0

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Solving a quadratic Inequality  Solve 9x−14−x2&amp;gt;0

marzembreax · Accepted Answer

Lets

Serifluinueyk · Accepted Answer

−9x−14−x2&amp;gt;0⇔x2+9x+14&amp;lt;0  Since △=81−4⋅14=25, the roots of LHS are x1,2=−9±52=−7,−2, so the inequality is (x+7)(x+2)&amp;lt;0⇒−7&amp;lt;x&amp;lt;−2

RizerMix · Accepted Answer

The general way is to use the formula ax2+bx+c=0⇒x1,2=−b2a±b2−4ac2a and see when the function equals zero. Since it is continuous, it is enough to check the sign of f(x) for some x1&amp;lt;x&amp;lt;x2. If it is positive, the f(x)&amp;gt;0 for x1&amp;lt;x&amp;lt;x2 and f(x)&amp;lt;0 otherwise. Similarly, if it is negative, the f(x)&amp;lt;0 for x1&amp;lt;x&amp;lt;x2 and f(x)&amp;gt;0 otherwise. The key is that a continuous function has the same sign between two zeroes, so the general way is to find all the zeroes (the xi where f(xi)=0) and then check by substitution what is its sign between each adjacent pair of them (xi,xi+1).

Solving a quadratic Inequality Solve 9x-14-x^{2}>0

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