Question

If a and f3 are zeroes of the quadratic polynomial ex" + 4x + 1, then find
quadratic polynomial whose zeroes are 2a and 2 f3

Answer 1

Α and β are the zeroes of 4x² + 4x +1 
a = 4 
b  =4 
c = 1
sum of zeroes = -b/a
α + β = -b/a
α+ β = -4 /4 
α + β = -1 ........................(i)

product of zeroes  = c/a
αβ = c/a
αβ = 1/4 ................(ii)


zeroes of polynomial are 2α and 2β
so 
sum of zeroes = 
2α + 2 β
2(α+β)         from (i)
2(-1)
-2

product of zeroes 
(2α)(2β)
4αβ
4 (1/4)                  from (ii)
1 

polynomial = 
x ² - ( sum of zeroes )x + product of zeroes
x² - (-2)x +1
x² +2 x+1