Question

if kx^2 +1-2(k-1)x + x^2 =0 has equal roots find k

Answer 1

Given: kx2 + 1-2(k-1)x + x2
sol;
=kx2 + x2 -2(k-1) +1
x2 (k+1) - 2(k-1) +1
here,
a=(k+1)   b= -2(k-1) & c= 1
for real and equal roots;
D=0
=b2- 4ac=0

Putting the values of a.b and c

[-2(k-1)]2 - 4 (k+1)(1)=0

then on opening the brackets we'll get;
(4k)(k-3)=0
=   4k=0             and        (k-3)=0
=     k=0               or           k=3