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Mathematics · 2024 · 2 marks
CBSE 2024 · Region 5 · Set 2 · Q21
If α and β are zeroes of the quadratic polynomial p ( x )= x^2-5 x +4, then find the value of 1/(α)+1/(β)-2 α β.
If $\displaystyle \alpha$ and $\displaystyle \beta$ are zeroes of the quadratic polynomial $\displaystyle \mathrm{p}(\mathrm{x})=\mathrm{x}^{2}-5 \mathrm{x}+4$, then find the value of $\displaystyle \frac{1}{\alpha}+\frac{1}{\beta}-2 \alpha \beta$.
Marking-scheme solution
\[\begin{aligned}
& \alpha+\beta=5 \\
& \alpha \beta=4 \\
& \begin{aligned}
\frac{1}{\alpha}+\frac{1}{\beta}-2 \alpha \beta & =\frac{\alpha+\beta}{\alpha \beta}-2 \alpha \beta \\
& =\frac{5}{4}-2 \times 4 \\
& =\frac{-27}{4}
\end{aligned}
\end{aligned}
\]
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CBSE Class 10 Mathematics past-paper question from the 2024 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.