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Mathematics · 2025 · 3 marks
CBSE 2025 · Region 4 · Set 1 · Q30
α and β are zeroes of a quadratic polynomial p x^2+q x+1. Form a quadratic polynomial whose zeroes are 2/(α) and 2/(β).
$\displaystyle \alpha$ and $\displaystyle \beta$ are zeroes of a quadratic polynomial $\displaystyle p x^{2}+q x+1$. Form a quadratic polynomial whose zeroes are $\displaystyle \frac{2}{\alpha}$ and $\displaystyle \frac{2}{\beta}$.
Marking-scheme solution
\(\displaystyle \alpha+\beta=-\frac{q}{p}, \alpha \beta=\frac{1}{p}\)
Sum of zeroes of the required polynomial \(\displaystyle =\frac{2}{\alpha}+\frac{2}{\beta}=2 \frac{(\beta+\alpha)}{\alpha \beta}=-2 q\)
Product of zeroes of the required polynomial \(\displaystyle =\frac{2}{\alpha} \times \frac{2}{\beta}=\frac{4}{\alpha \beta}=4 p\)
∴ required polynomial is \(\displaystyle x^{2}+2 q x+4 p\)
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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.