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


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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 = −2, −5 Therefore, α = -2 & β = −5 are the zeroes of polynomial Splitting the middle term method We need to find two numbers whose Sum = 7 Product = 10 × 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 = − (𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑥)/(𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑥2) i.e. α + β = - 𝒃/𝒂 Product of zeroes = (𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑡𝑒𝑟𝑚)/(𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑥2) i.e. α × β = 𝒄/𝒂 α + β = −2 + (−5) = −2 − 5 = –7 − 𝑏/𝑎 = − 7/1 = −7 α β = (−2) ( −5) = 10 𝑐/𝑎 = 10/1 = 10 Since, L.H.S = R.H.S Hence relationship between zeroes & coefficient is verified

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.