Question

If alpha and beta are the zeroes of the polynomial such that α+β=6 and αβ=4, then write the polynomial.

Answer 1

alpha & beta are the zeros of the polynomial and 
α+β=6 and αβ=4
therefore the required polynomial is x^2 - (α+β)x + αβ = 0
                                                 =x^2 - 6x + 4 = 0
x^2 - 6x + 4 = 0 is the required polynomial.

Answer 2

to get this quadratic equation in polynomial form , it can be written as 

α + β = 6  ,  α β = 4

x^2 - ( α + β) x + αβ = 0
 x^2 - 6 x  + 4 = 0