3) For what value of p the equation (1 + p) x
2 + 2(1 + 2p) x + (1 + p) = 0 has coincident roots

Question

Manbar Singh · Accepted Answer

The given quadratic equation is:1 + p x2 + 2 1 + 2p x + 1 + p = 0We have,a = 1 + pb = 2 1 + 2pc = 1 + pNow, D = b2 - 4 ac= 2 1 + 2p2 - 4 1 + p 1 + p= 4 1 + 4p2 + 4p - 4 1 + p2 + 2p= 4 + 16p2 + 16p - 4 - 4p2 - 8p= 12p2 + 8pFor coincident roots,      D = 0⇒ 12p2 + 8p = 0⇒ 4p 3p + 2 = 0⇒ p = 0     or    3p + 2 = 0⇒ p = 0      or     p = -23

3) For what value of p the equation (1 + p) x2 + 2(1 + 2p) x + (1 + p) = 0 has coincident roots

3) For what value of p the equation (1 + p) x
2 + 2(1 + 2p) x + (1 + p) = 0 has coincident roots