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 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.