Ex 2.2, 1 (i) - 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. x2 – 2x – 8 Let p(x) = x2 – 2x – 8 Zero of the polynomial is the value of x where p(x) = 0 Putting p(x) = 0 x2 – 2x – 8 = 0 We find roots using splitting the middle term method x2 – 4x + 2x – 8 = 0 x(x – 4) + 2(x – 4) = 0 (x + 2)(x − 4) = 0 So x = −2, 4 Splitting the middle term method We need to find two numbers where Sum = -2 Product = −8 × 1 = −8 Verifying relationship b/w zeroes and coefficients p(x) = x2 − 2x − 8 = 1x2 − 2x − 8 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 α + β = −2 + 4 = 4 − 2 = 2 − 𝑏/𝑎 = − ((−2))/1 = 2 α β = (−2) × 4 = −8 𝑐/𝑎 = (−8)/1 = −8 Since, L.H.S = R.H.S Hence relationship between zeroes & coefficient is verified