Question

If the equations x² + px + q = 0 and x² + p’x + q’ = 0 have a common root, show that it must be equal to (pq' - p'q/q - q') or (q - q'/p' - p)

Answer 1

If α is the common root, then. 

α² + pα + q = 0 ……. (1) 

α² + p’α + q’ = 0 ……… (2) 

Subtracting α (p – p’) = q’ – q

α = (pq' - p'q/q - q') = (q - q'/p' - p) ... (3)

Eliminating α from (1) & (2)