Question
Form the quadratic equation from the roots given below : $\frac{1}{2},-\frac{1}{2}$
✓
Answer
Let $\alpha=\frac{1}{2}$ and $\beta=-\frac{1}{2}$
$\therefore \alpha+\beta=\frac{1}{2}-\frac{1}{2}=0 \text { and } \alpha \beta=\frac{1}{2} \times-\frac{1}{2}=-\frac{1}{4}$
$\therefore$ and quadratic equation is, $x^2-(\alpha+\beta) x+\alpha \beta=0$
$\begin{array}{l}
\therefore x ^2-(0) x +\left(-\frac{1}{4}\right)=0 \\
\therefore x ^2-\frac{1}{4}=0 \\
\therefore 4 x ^2-1=0
\end{array}$
$\therefore \alpha+\beta=\frac{1}{2}-\frac{1}{2}=0 \text { and } \alpha \beta=\frac{1}{2} \times-\frac{1}{2}=-\frac{1}{4}$
$\therefore$ and quadratic equation is, $x^2-(\alpha+\beta) x+\alpha \beta=0$
$\begin{array}{l}
\therefore x ^2-(0) x +\left(-\frac{1}{4}\right)=0 \\
\therefore x ^2-\frac{1}{4}=0 \\
\therefore 4 x ^2-1=0
\end{array}$
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