✓ Board-verified
Mathematics · 2026 · 2 marks
CBSE 2026 · Region 1 · Set 3 · Q24
Find a quadratic polynomial whose zeroes are (5-2 √ 3 ) and (5+2 √ 3 ).
Find a quadratic polynomial whose zeroes are $\displaystyle (5-2 \sqrt{3})$ and $\displaystyle (5+2 \sqrt{3})$.
Marking-scheme solution
Let \(\displaystyle \alpha\) and \(\displaystyle \beta\) be the zeroes of the required polynomial.
\[\begin{aligned}
& \alpha=5-2 \sqrt{3}, \beta=5+2 \sqrt{3} \\
& \alpha+\beta=10 \\
& \alpha \beta=13 \\
& \therefore \text { The quadratic polynomial is } x^{2}-10 x+13
\end{aligned}
\]
More from Polynomials
- A polynomial p(x), which has sum of its zeroes equal to their product, is:2026
- If α, β are the zeroes of the polynomial p(x)=x^2-3 x-1, then find the value of 1/(α)+1/(β).2026
- Find the zeroes of the quadratic polynomial x^2-15 and verify the relationship between the zeroes and the coefficients of the polynomial.2024
- If α, β are zeroes of the polynomial x^2-1, then value of (α+β) is:2023
- If α and β are the zeroes of the polynomial p(x)=x^2-a x-b, then the value of (α+β+α β) is equal to:2025
- If one zero of the polynomial p(x)=6 x^2+37 x-(k-2) is reciprocal of the other, then find the value of k.2023
- 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+1.2025
- If α and β are the zeroes of the polynomial a x^2-x+c. Obtain a polynomial whose zeroes are α-3 and β-3.2025
CBSE Class 10 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.