Ex 2.2, 1 (vi) - 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. (vi) 3x2 – x – 4 Let p(x) = 3x2 – x – 4 Zero of the polynomial is the value of x where p(x) = 0 Putting p(x) = 0 3x2 − x – 4 = 0 We find roots using splitting the middle term method 3x2 – 4x + 3x – 4 = 0 x(3x – 4) + 1(3x - 4) = 0 (3x – 4)(x + 1) = 0 Splitting the middle term method We need to find two numbers where Sum = -1 Product = -4 × 3 = -12 So x = 𝟒/𝟑 , x = – 1 Therefore, α = 𝟒/𝟑 & β = – 1 are the zeroes of the polynomial Now, verifying zeroes Verifying relationship b/w zeroes and coefficients p(x) = 3x2 − x − 4 = 3x2 − 1x − 4 Comparing with ax2 + bx + c a = 3 , We have to verify Sum of zeroes = − (𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑥)/(𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑥2) i.e. α + β = - 𝒃/𝒂 α + β = 4/3 + (−1) = 𝟏/𝟑 − 𝑏/𝑎 = −((−1))/3 = 𝟏/𝟑 α β = 4/3 × (−1) = (−𝟒)/𝟑 𝑐/𝑎 = (−𝟒)/𝟑 Since, L.H.S = R.H.S Hence relationship between zeroes & coefficient is verified