Question

(K-2)x^2+2(2k-3)x+(5k-6)=0 has equal roots then find k

Answer 1

The given equation is (k-2)x^2+2(2k-3)x+(5k-6) and the roots are real and equal. 
here a=k-2 
b=4k-6 
c=5k-6 
we konw that 
D= b^2-4ac 
putting the value of a,b and c 
D=(4k-6)^2-4×(k-2)(5k-6) 
D=16k^2+36-48k-20k^2+64k-48 
D=4k^2-16k+12 
taking common 4 

acc. to question 
k^2-4k+3=0 
factories this eq. 
(k-3)(k-1)=0 
k=3,1

I hope this will help you