xafeguerpf3l

2023-02-24

Find the root(s) of the quadratic equation $2{x}^{2}+5x-12=0$

Cheyenne Lynn

So we have $2{x}^{2}+5x-12=0$
Let $\alpha ,\beta$ be the roots of the equation $a{x}^{2}+bx+c=0$
Then $\alpha =\frac{-b-\sqrt{D}}{2a}$
$\beta =\frac{-b-\sqrt{D}}{2a}$
Here, $D={5}^{2}-4\left(2\right)\left(-1\right)=121\phantom{\rule{0ex}{0ex}}⇒\sqrt{D}=11\phantom{\rule{0ex}{0ex}}\alpha =\frac{-5+11}{2×2}=\frac{3}{2}\phantom{\rule{0ex}{0ex}}\beta =\frac{-5-11}{2×2}=-4$

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