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Mathematics · 2025 · 3 marks
CBSE 2025 · Region 5 · Set 1 · Q27
Obtain the zeroes of the polynomial 7 x^2+18 x-9. Hence, write a polynomial each of whose zeroes is twice the zeroes of given polynomial.
Obtain the zeroes of the polynomial $\displaystyle 7 x^{2}+18 x-9$. Hence, write a polynomial each of whose zeroes is twice the zeroes of given polynomial.
Marking-scheme solution
\[\begin{aligned}
& 7 x^{2}+18 x-9 \\
= & (7 x-3)(x+3) \\
\therefore & \text { Zeroes are }-3, \frac{3}{7}
\end{aligned}
\]
New zeroes are \(\displaystyle -6, \frac{6}{7}\)
Sum of new zeroes \(\displaystyle =(-6)+\frac{6}{7}=-\frac{36}{7}\)
Product of new zeroes \(\displaystyle =(-6) \times \frac{6}{7}=-\frac{36}{7}\)
∴ Required polynomial is \(\displaystyle x^{2}+\frac{36}{7} x-\frac{36}{7}\) or \(\displaystyle 7 x^{2}+36 x-36\)
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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.