Polynomials
CBSE 2026 Board Exam Set 3 (Code 30/1/3)
CBSE_BOARD_PYQ_2026_30_1_3
Grade 10
Question:
[Section B]
Find a quadratic polynomial whose zeroes are $5 - 2\sqrt{3}$ and $5 + 2\sqrt{3}$.
Step-by-Step Solution
Key Concept: $p(x) = x^2 - (\alpha + \beta)x + \alpha \beta$.
Sum of zeroes $\alpha + \beta = (5-2\sqrt3) + (5+2\sqrt3) = 10$. Product $\alpha \beta = (5-2\sqrt3)(5+2\sqrt3) = 25 - 12 = 13$. Quadratic polynomial is $x^2 - 10x + 13$. [2.0 Marks]
Correct Answer: x² - 10x + 13
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