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 = −2, −5
Therefore,
α = -2 & β = −5 are the zeroes of polynomial
p(x) = x2 + 7x + 10
= 1x2 + 7x + 10
Comparing with ax2 + bx + c
So a = 1 ,
We have to 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

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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