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

Transcript

Ex 2.2, 1 Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. (v) t2 - 15 Let p(t) = t2 – 15 Zero of the polynomial is the value of t where p(t) = 0 Putting p(t) = 0 t2 – 15 = 0 (t)2 – (√15)2 = 0 Using a2 – b2 = (a – b)(a + b) (t − √15)(t + √15) = 0 So t = √𝟏𝟓 , – √𝟏𝟓 Verifying relationship b/w zeroes and coefficients p(t) = t2 – 15 = t2 + 0 – 15 = 1t2 + 0(t) – 15 It is of the form at2 + bt + c ∴ a = 1, We have to verify Sum of zeroes = − (𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑥)/(𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑥2) i.e. α + β = - 𝑏/𝑎 α + β = √15 − √15 = 0 − 𝑏/𝑎 = − 0/1 = 0 α β = (√15) (–√15) = –(√15)2 = –15 𝑐/𝑎 = (−15)/1 = –15 Since, L.H.S = R.H.S Hence relationship between zeroes & coefficient is verified