Question

The roots of the equation 2x² – 7x + 5 = 0 are α and β. Without solving the root find

(i) 1/α + 1/β

(ii) α/β + β/α 

(iii) (α + 2)/(β + 2) + (β + 2)/(α + 2)

Answer 1

2x² – 7x + 5 = x² – (7/2)x + (5/2) = 0

α + β = 7/2

αβ = 5/2

(i) 1/α + 1/β

(ii) α/β + β/α 

(iii) (α + 2)/(β + 2) + (β + 2)/(α + 2)