This is the basic and exam oriented question from polynomials in which we have zeroes of the quadratic polynomial and we have to find the quadratic polynomial and have to find the relation between the coefficients and the zeroes of the polynomial.
Kindly give me a detailed solution of this question
RS Aggarwal, Class 10, chapter 2A, question no 13
Let α=2 and β=−6
Sum of the zeroes = (α+β)=2−6=−4
Product of the zeroes , αβ=2(−6)=−12
Required quadratic polynomial is
x²−(α+β)x+αβ=x²−(−4)x−12
=x²+4x−12
and
sum of the zeroes =−4=−4/1=(coefficient of x)/(−coefficient of x²)
product of zeroes =−12×1=−12/1=constant term/coefficient of x²