Question
Obtain the quadratic equation if roots are $-3,-7$.
✓
Answer
Let $\alpha=-3$ and $\beta=-7$
$
\begin{array}{l}
\therefore \alpha+\beta=(-3)+(-7)=-10 \text { and } \alpha \times \beta=(-3) \times(-7)=21 \\
\therefore \text { and quadratic equation is, } x^2-(\alpha+\beta) x+\alpha \beta=0 \\
\therefore x^2-(-10) x+21=0 \\
\therefore x^2+10 x+21=0
\end{array}
$
$
\begin{array}{l}
\therefore \alpha+\beta=(-3)+(-7)=-10 \text { and } \alpha \times \beta=(-3) \times(-7)=21 \\
\therefore \text { and quadratic equation is, } x^2-(\alpha+\beta) x+\alpha \beta=0 \\
\therefore x^2-(-10) x+21=0 \\
\therefore x^2+10 x+21=0
\end{array}
$
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