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 November 25, 2025 by Teachoo
Transcript
Question 28 Find the zeroes of the quadratic polynomial 2š„2 ā (1 + 2ā2) š„ + ā2 and verify the relationship between the zeroes and coefficients of the polynomial.Let p(x) = 2š„2 ā (1 + 2ā2) š„ + ā2 Zero of the polynomial is the value of x where p(x) = 0 Putting p(x) = 0 2š„2 ā (1 + 2ā2) š„ + ā2 = 0 We find roots using splitting the middle term method 2x2 ā x ā 2āš x + āš = 0 x(2x ā 1) ā ā2(2x ā 1) = 0 Splitting the middle term method We need to find two numbers where Sum = 1 + 2ā2 Product = 2 Ć ā2 = 2 ā2 (x ā āš)(2x ā 1) = 0 Thus, our roots are x = āš, and x =š/š Verifying relationship b/w zeroes and coefficients p(x) = 2š„2 ā (1 + 2ā2) š„ + ā2 Comparing with ax2 + bx + c a = 2 , b = ā(1 + 2āš), c = āš We have to verify Sum of zeroes = ā (š¶šššššššššš” šš š„)/(š¶šššššššššš” šš š„2) i.e. Ī± + Ī² = ā š/š Since, L.H.S = R.H.S Hence relationship between zeroes & coefficient is verified Product of zeroes = (š¶ššš š”ššš” š”ššš)/(š¶šššššššššš” šš š„2) i.e. Ī± Ć Ī² = š/š
