If α and β are the zeroes of the polynomial 4x2-4x+1, then 1/α + 1/β is . . .

Question : If α and β are the zeroes of the polynomial 4x²-4x+1, then 1/α + 1/β is ____________.

Doubt by Gauri 

Solution : 

4x²-4x+1

a = 4

b=-4

c=1

We know, 
α + β = -b/a
α + β = -(-4)/4
α + β = 1 — (1)

α β = c/a
α β = 1/4 — (2)

Now, 
1/α + 1/β
= (β+α)/αβ
= (α+β)/αβ
= (1)/(1/4) [From eq (1) and eq (2)]
= 4×1

= 4

∴ 1/α + 1/β = 4