Slide18.JPG

Slide19.JPG
Slide20.JPG Slide21.JPG

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


Transcript

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

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

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.