Check sibling questions

Slide7.JPG

Slide8.JPG
Slide9.JPG

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


Transcript

Example 2 Find the zeroes of the quadratic polynomial x2 + 7x + 10, and verify the relationship between the zeroes and the coefficients. Let p(x) = x2 + 7x + 10 Zero of the polynomial is the value of x where p(x) = 0 Putting p(x) = 0 x2 + 7x + 10 = 0 We find roots using splitting the middle term method x2 + 2x + 5x + 10 = 0 x(x + 2) + 5(x + 2) = 0 (x + 2)(x + 5) = 0 So, x = βˆ’2, βˆ’5 Therefore, Ξ± = -2 & Ξ² = βˆ’5 are the zeroes of polynomial Splitting the middle term method We need to find two numbers whose Sum = 7 Product = 10 Γ— 1 = 10 Verifying relationship b/w zeroes and coefficients p(x) = x2 + 7x + 10 = 1x2 + 7x + 10 Comparing with ax2 + bx + c a = 1 , We have to verify Sum of zeroes = βˆ’ (πΆπ‘œπ‘’π‘“π‘“π‘–π‘π‘–π‘’π‘›π‘‘ π‘œπ‘“ π‘₯)/(πΆπ‘œπ‘’π‘“π‘“π‘–π‘π‘–π‘’π‘›π‘‘ π‘œπ‘“ π‘₯2) i.e. Ξ± + Ξ² = - 𝒃/𝒂 Product of zeroes = (πΆπ‘œπ‘›π‘ π‘‘π‘Žπ‘›π‘‘ π‘‘π‘’π‘Ÿπ‘š)/(πΆπ‘œπ‘’π‘“π‘“π‘–π‘π‘–π‘’π‘›π‘‘ π‘œπ‘“ π‘₯2) i.e. Ξ± Γ— Ξ² = 𝒄/𝒂 Ξ± + Ξ² = βˆ’2 + (βˆ’5) = βˆ’2 βˆ’ 5 = –7 βˆ’ 𝑏/π‘Ž = βˆ’ 7/1 = βˆ’7 Ξ± Ξ² = (βˆ’2) ( βˆ’5) = 10 𝑐/π‘Ž = 10/1 = 10 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.