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Quadratic Equations in One Variable — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsQuadratic Equations in One Variable2 Marks
Question
Solve equation by factorisation : $
\sqrt{3} x^2+10 x+7 \sqrt{3}=0
$
✓

Answer

$
\begin{aligned}
& \sqrt{3} x^2+10 x+7 \sqrt{3}=0 \\
& \Rightarrow \sqrt{3} x^2+3 x+7 x+7 \sqrt{3}=0 \\
& \Rightarrow \sqrt{3} x(x+\sqrt{3})+7(x+\sqrt{3})=0 \\
& \Rightarrow(x+\sqrt{3})(\sqrt{3}+7)=0
\end{aligned}
$
Either $x+\sqrt{3}=0$,
then $x =-\sqrt{3}$
or
$
\sqrt{3} x+7=0 \text {, }
$
then $\sqrt{3} x=-7$
$
\begin{aligned}
& \Rightarrow x =\frac{-7}{\sqrt{3}} \\
& x =\frac{-7 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}} \\
& =\frac{-7 \sqrt{3}}{3}
\end{aligned}
$
Hence $x =-\sqrt{3}, \frac{-7 \sqrt{3}}{3}$.

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