Question

Find the value of p such that the wuadratic equation (p-12)x² - 2(p-12)x+2=0 has equal roots

Answer 1

(P -12)x² +2( P -12) x + 2 =0 have two real and equal roots so,
D = b² -4ac =0

here,
b = 2( P -12)
a = (P -12)
c = 2
now,
D = {2(P -12)}² -4.2(P -12) =0
4{ (P -12)² -2( P -12) } =0
(P -12)² -2(P -12)=0
(P -12){ P -12 -2} = 0
(P -12)( P -14) =0
P = 12, 14

hence value of P = 12, 14