CBSE Class 10 Sample Paper for 2026 Boards - Maths Standard
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CBSE Class 10 Sample Paper for 2026 Boards - Maths Standard
Last updated at August 14, 2026 by Teachoo
Transcript
Question 28 Find the zeroes of the quadratic polynomial 2𝑥2 – (1 + 2√2) 𝑥 + √2 and verify the relationship between the zeroes and coefficients of the polynomial.Let p(x) = 2𝑥2 – (1 + 2√2) 𝑥 + √2 Zero of the polynomial is the value of x where p(x) = 0 Putting p(x) = 0 2𝑥2 – (1 + 2√2) 𝑥 + √2 = 0 We find roots using splitting the middle term method 2x2 – x – 2√𝟐 x + √𝟐 = 0 x(2x – 1) – √2(2x – 1) = 0 Splitting the middle term method We need to find two numbers where Sum = 1 + 2√2 Product = 2 × √2 = 2 √2 (x – √𝟐)(2x − 1) = 0 Thus, our roots are x = √𝟐, and x =𝟏/𝟐 Verifying relationship b/w zeroes and coefficients p(x) = 2𝑥2 – (1 + 2√2) 𝑥 + √2 Comparing with ax2 + bx + c a = 2 , b = –(1 + 2√𝟐), c = √𝟐 We have to verify Sum of zeroes = − (𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑥)/(𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑥2) i.e. α + β = – 𝒃/𝒂 Since, L.H.S = R.H.S Hence relationship between zeroes & coefficient is verified Product of zeroes = (𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑡𝑒𝑟𝑚)/(𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑥2) i.e. α × β = 𝒄/𝒂
