One of the most important and exam oriented question from polynomials in which we have given the sum and the product of 2 zeroes and we have to find the zeroes of the polynomial and also asked to find the quadratic polynomial.

Kindly solve the above problem

RS Aggarwal, Class 10, chapter 2A, question no 16

## Given: Sum fo zeroes =Â Â (Î±+Î²)=8

Product of the zeroes =Â Î±Î²=12

Required quadratic polynomial is

xÂ²âˆ’(Î±+Î²)x+Î±Î²=xÂ²âˆ’(8)x+12

Now , find the zeroes of the above polynomial.

LetÂ f(x)=xÂ²âˆ’(8)x+12

=Â xÂ²âˆ’6xâˆ’2x+12

=(xâˆ’6)(xâˆ’2)

SubstituteÂ f(x)=0

(xâˆ’6)=0Â orÂ (xâˆ’2)=0

â‡’x=6Â orÂ x=2