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

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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