Let α and β be the roots of equation p x 2 + q x + r = 0 , p ≠ 0 . If p , q , r are in A.P. and 1 α + 1 β = 4 , then the value of α - β is

Step-by-step solution

1 α + 1 β = 4 α + β α β = 4 ∴     - q p r p = 4 ∴    - q r = 4 p ,   q ,   r are in A.P. Let p = a - d   ;   q = a ,   r = a + d . ∴     - a a + d = 4   ⇒   - a = 4 a + 4 d   ⇒   d = - 5 a 4 p = a + 5 a 4 = 9 a 4 ;   q = a ,   r = a - 5 a 4 = - a 4 ∴     9 4 x 2 + 4 4 x - 1 4 = 0 ∴    9 x 2 + 4 x