Question 27 - CBSE Class 10 Sample Paper for 2020 Boards - Maths Basic
Last updated at Oct. 24, 2019 by Teachoo

Find the zeroes of the quadratic polynomial x
^{
2
}
− 3x − 10 and verify the relationship between the zeroes and coefficient.

Note
: This
is similar
to Ex 2.2, 1 of NCERT – Chapter 2 Class 10

Check the answer here
https://www.teachoo.com/1489/494/Ex-2.2--1---Find-zeroes-of-following-quadratic-polynomials/category/Ex-2.2/

Transcript

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

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