For equal roots, b2−4ac=0b^{2} - 4ac = 0b2−4ac=0
From the equation, a=P,b=(P+1),c=Pa = P, b = (P+1), c = Pa=P,b=(P+1),c=P
(P+1)2−4(P)(P)=P2+2P+1−4P2=0(P+1)^{2} - 4(P)(P) = P^{2} + 2P + 1 - 4P^{2} = 0(P+1)2−4(P)(P)=P2+2P+1−4P2=0
−3P2+2P+1=0 ⟹ 3P2−2P−1=0-3P^{2} + 2P + 1 = 0 \implies 3P^{2} - 2P - 1 = 0−3P2+2P+1=0⟹3P2−2P−1=0
3P2−3P+P−1=03P^{2} - 3P + P - 1 = 03P2−3P+P−1=0
3P(P−1)+1(P−1)=03P(P - 1) + 1(P - 1) = 03P(P−1)+1(P−1)=0
P=1 or −13P = \text{1 or } \frac{-1}{3}P=1 or 3−1