Question

If  5p² - 7p - 3 = 0 and 5q² - 7q - 3 = 0,  p ≠ q , then the equation whose roots are 5p– 4q and 5q – 4p is :

(A)   5x² + x - 439 = 0

(B)   5x² + 7x - 439 = 0

(C)   5x² - 7x - 439 = 0

(D)   5x² + 7x + 439 = 0

Answer 1

Correct option  (C) 5x² - 7x - 439 =  0

Explanation:

Obviously p,q satisfy the equation 5x² - 7x - 3 =  0.

Hence  p + q = 7/5, pq = -3/5

given α = 5p - 4q & β = 5q - 4p.

The required equation

x² - (α + β) x + αβ = 0

5x² + 7x - 439 =  0