Question

find the quadratic polynomial of the zeros of its are 1/2 and 3/2 respectively

Answer 1

Given zeroes of a polynomial are 
α = 1/2 , β = 3/2
we know that when α and β are the zeroes of a polynomial then the polynomial is 
K[x² - (α+β)x + αβ]
here α+β = 1/2  + 3/2
                = (1+3)/2
                = 4/2
                = 2
αβ = (1/2)(3/2)
     = 3/4
now substituting these values in the formula
K[ x² - (α+β)x + αβ]
=K[ x² - (2)x + 3/4]
=K[ x² - 2x +3/4]
=K[ (4x² - 2x + 3)/4]
Let take K = 4 to remove the fraction form of it
4[ (4x² - 2x + 3)/4]
= 4x² -2x +3
∴4x² - 2x + 3 is the quadratic polynomial