Ex 2.2, 1 (ii) - Chapter 2 Class 10 Polynomials

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Ex 2.2, 1 Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. (ii) 4s2 – 4s + 1 Let p(s) = 4s2 – 4s + 1 Zero of the polynomial is the value of s where p(s) = 0 Putting p(s) = 0 4s2 – 4s + 1 = 0 We find roots using splitting the middle term method 4s2 – 4s + 1 = 0 4s2 – 2s – 2s + 1 = 0 2s(2s – 1) – 1(2s – 1) = 0 Splitting the middle term method We need to find two numbers whose Sum = –4 Product = 1 × 4 = 4 (2s – 1) (2s – 1) = 0 So, s = 𝟏/𝟐 , 𝟏/𝟐 Therefore , α = 𝟏/𝟐 & β = 𝟏/𝟐 are roots of the polynomial Now, verifying zeroes Verifying relationship b/w zeroes and coefficients p(x) = 4s2 – 4s + 1 Comparing with as2 + bs + c a = 4 , We have to verify Sum of zeroes = − (𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑥)/(𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑥2) i.e. α + β = - 𝒃/𝒂 α + β = 1/2 + 1/2 = 1 − 𝑏/𝑎 = − ((−4))/4 = 1 α β = 1/2 × 1/2 = 𝟏/𝟒 𝑐/𝑎 = 𝟏/𝟒 Since, L.H.S = R.H.S Hence relationship between zeroes & coefficient is verified