Question

If P(x) = x2 + 5x + p and g(x) = x

2 + 3x + q have a common factor, then prove that (p – q)2 = 2(3p – 5q)​

Answer 1

Step-by-step explanation:

let a common factor be x-k

then p ( k) = q ( k)

k2 + 5k + p = k 2 + 3k + q

5k - 3k = q - p

2k = q - p

k = q-p / 2

substitute k value in p ( k) = 0

( q - p)2 /4 + 5 ( q - p)/ 2 + p = 0

( q -p) 2+ 10q - 10 p + 4p = 0

( q-p)2 + 10 q - 6 p = 0

( q-p )2 = 6p - 10q

( q-p) 2 = 2 ( 3p -5q)

(p -q) 2 = 2 ( 3p - 5q)

Answer 2

Hi... Hope this helps you....