Ex 2.2, 1(i)
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
Therefore, α = – 2 & β = 4 are the zeroes of the polynomial
p(x) = x2 – 2x – 8
= 1x2 – 2x – 8
Comparing with ax2 + bx + c
So a = 1 ,
We verify
Sum of zeroes = − (𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑥)/(𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑥2)
i.e. α + β = - 𝑏/𝑎
Since, L.H.S = R.H.S
Hence relationship between zeroes & coefficient is verified

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.