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Mathematics · 2022 · 2 marks
CBSE 2022 · Region 1 · Set 1 · Q3
(a) Find the value of m for which the quadratic equation (m-1) x^2+2(m-1) x +1=0 has two real and equal roots.
(a)
Find the value of m for which the quadratic equation \[(m-1) \mathrm{x}^{2}+2(m-1) \mathrm{x}+1=0 \] has two real and equal roots.
OR
(b)
Solve the following quadratic equation for x : $\displaystyle \sqrt{3} \mathrm{x}^{2}+10 \mathrm{x}+7 \sqrt{3}=0$
Marking-scheme solution
(a)
For real and equal roots
\[\begin{aligned}
& 4(m-1)^{2}-4(m-1)=0 \\
& \Rightarrow m=1 \text { or } m=2 \\
& m \neq 1 \Rightarrow m=2
\end{aligned}
\]
Or
\[\sqrt{3} x^{2}+10 x+7 \sqrt{3}=0
\] or \(\displaystyle \sqrt{3} x^{2}+3 x+7 x+7 \sqrt{3}=0\)
or \(\displaystyle (\sqrt{3} x+7)(x+\sqrt{3})=0\)
\[\Rightarrow \quad x=-\frac{7}{\sqrt{3}},-\sqrt{3} \text { or }-\frac{7}{3} \sqrt{3},-\sqrt{3}
\]
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CBSE Class 10 Mathematics past-paper question from the 2022 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.