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Mathematics · 2025 · 3 marks
CBSE 2025 · Region 4 · Set 2 · Q26
α and β are zeroes of a quadratic polynomial x^2-a x-b. Obtain a quadratic polynomial whose zeroes are 3 α+1 and 3 β+1.
$\displaystyle \alpha$ and $\displaystyle \beta$ are zeroes of a quadratic polynomial $\displaystyle x^{2}-a x-b$. Obtain a quadratic polynomial whose zeroes are $\displaystyle 3 \alpha+1$ and $\displaystyle 3 \beta+1$.
Marking-scheme solution
\[\alpha+\beta=a, \alpha \beta=-b
\]
Sum of zeroes of required polynomial
\[=(3 \alpha+1)+(3 \beta+1)
\]
\[\begin{aligned}
& =3(\alpha+\beta)+2 \\
& =3 a+2 \\
& \text { Product of zeroes of required polynomial } \\
& =(3 \alpha+1)(3 \beta+1) \\
& =9 \alpha \beta+3(\alpha+\beta)+1 \\
& =-9 b+3 a+1 \\
& \therefore \text { The required polynomial is } x^{2}-(3 a+2) x+(3 a-9 b+1)
\end{aligned}
\]
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CBSE Class 10 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.