Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

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Last updated at Aug. 8, 2023 by Teachoo

Example 2 Find the zeroes of the quadratic polynomial x2 + 7x + 10, and verify the relationship between the zeroes and the coefficients. Let p(x) = x2 + 7x + 10 Zero of the polynomial is the value of x where p(x) = 0 Putting p(x) = 0 x2 + 7x + 10 = 0 We find roots using splitting the middle term method x2 + 2x + 5x + 10 = 0 x(x + 2) + 5(x + 2) = 0 (x + 2)(x + 5) = 0 So, x = β2, β5 Therefore, Ξ± = -2 & Ξ² = β5 are the zeroes of polynomial Splitting the middle term method We need to find two numbers whose Sum = 7 Product = 10 Γ 1 = 10 Verifying relationship b/w zeroes and coefficients p(x) = x2 + 7x + 10 = 1x2 + 7x + 10 Comparing with ax2 + bx + c a = 1 , We have to verify Sum of zeroes = β (πΆππππππππππ‘ ππ π₯)/(πΆππππππππππ‘ ππ π₯2) i.e. Ξ± + Ξ² = - π/π Product of zeroes = (πΆπππ π‘πππ‘ π‘πππ)/(πΆππππππππππ‘ ππ π₯2) i.e. Ξ± Γ Ξ² = π/π Ξ± + Ξ² = β2 + (β5) = β2 β 5 = β7 β π/π = β 7/1 = β7 Ξ± Ξ² = (β2) ( β5) = 10 π/π = 10/1 = 10 Since, L.H.S = R.H.S Hence relationship between zeroes & coefficient is verified