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Mathematics · 2022 · 2 marks
CBSE 2022 · Region 3 · Set 2 · Q4
(a) For what value of m, the quadratic equation m x^2-2(m-1) x+(m+2)=0 has two real and equal roots?
(a)
For what value of m, the quadratic equation \[m x^{2}-2(m-1) x+(m+2)=0 \] has two real and equal roots ?
OR
(b)
The diagonal of a rectangular field is $\displaystyle 60$ metres more than the shorter side. If the longer side is $\displaystyle 30$ metres more than the shorter side, find the sides of the field.
Marking-scheme solution
For equal roots \(\displaystyle 4(m-1)^{2}-4 m(m+2)=0\)
\[\Rightarrow m=\frac{1}{4}
\]
Or
Let shorter side be x m
\[(x+60)^{2}=x^{2}+(x+30)^{2}
\]
\(\displaystyle x^{2}-60 x-2700=0\)
x=$\displaystyle 90$
Sides are 90m,120m,150m
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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.