This is the basic and conceptual question from polynomials in which we have been asked to find the quadratic polynomial and also asked to find the zeroes of the polynomial if the sum of zeroes of the polynomial is 5/2 and their product is 1.
Kindly give me a detailed solution of this question
RS Aggarwal, Class 10, chapter 2A, question no 17
Given :-
α+β=5/2
αβ=1
P(x)=x²−(α+β)x+αβ
P(x)=x²−5x/2+1
=2x²−5x+2
P(x)=0
2x²−5x+2=0
2x²−4x−x+2=0
2x(x−2)−1(x−2)=0
(2x−1)(x−2)=0
2x−1=0 & x−2=0
x=1/2 & x=2 are zeros of P(x)