This is the basic and conceptual question from polynomials in which we have to find the quadratic polynomial and also the zeroes of the polynomial if their sum is 0 and their product is -1.
Kindly solve the above problem
RS Aggarwal, Class 10, chapter 2A, question no 15
Given : Sum fo zeroes = (α+β)=0
Product of the zeroes = αβ=−1
Required quadratic polynomial is
x²−(α+β)x+αβ=x²−(0)x−1
=x²−1
Now, find the zeroes of the above polynomial.
Let f(x)=x²−1
= x²−1²
=(x−1)(x+1)
Substitute f(x)=0
(x−1)=0 or (x+1)=0
⇒x=1 or x=−1
1 and −1 are the zeroes of the polynomial.