CBSE BoardEnglish MediumSTD 10MathsQuadratic Equations1 Mark
Question
Solve the quadratic equation $2 x^2+a x-a^2=0$ for $x$.
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Answer
Given $2 x^2+a x-a^2=0$Comparing the given equation with the standard quadratic equation $\left(a x^2+b x+c=0\right)$, we get $a=2, b=a$ and $c=-a^2$ Using the quadratic formula, $x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}$, we get: $x=\frac{-a \pm \sqrt{a^2-4 \times 2\left(-a^2\right)}}{2 \times 2}=\frac{-\alpha \pm \sqrt{9 a^2}}{4}$ $x=\frac{-\alpha+3 a}{4}=\frac{a}{2}$ and $x=\frac{-\alpha-3 a}{4}=-a$ So, the solutions of the given quadratic equation are $x=\frac{a}{2}$ and $x=-a$
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