Question 27 Find the zeroes of the quadratic polynomial x2 − 3x − 10 and verify the relationship between the zeroes and coefficient.
Let p(x) = x2 − 3x − 10
Finding zeroes by putting
p(x) = 0
x2 – 3x – 10 = 0
We find roots using splitting the middle term method
x2 – 5x + 2x – 10 = 0
x(x – 5) + 2(x – 5) = 0
(x + 2) (x – 5) = 0
So, x = –2, 5
Splitting the middle term method
We need to find two numbers whose
Sum = –3
Product = 1 × –10 = –10
So, zeroes are –2 and 5
Now, lets verify the relationship
p(x) = x2 − 3x − 10
Sum of zeroes
Sum of zeroes = − (𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑥)/(𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑥2)
LHS
–2 + 5
= 3
RHS
(−𝑏)/𝑎
= (−(−3))/1
= 3
Product of zeroes
Product of zeroes = (𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑡𝑒𝑟𝑚)/(𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑥2)
LHS
–2 × 5
= –10
RHS
𝑐/𝑎
= (−10)/1
= –10
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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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