Question

solve the following system of differmtial equation using operator method. ​

Answer 1

Answer:

i)  

If 2x  

2

+kx+3=0 has equal roots, then b  

2

−4ac=0.

Here, a=2,b=k,c=3

x  

2

+kx+3=0

b  

2

−4ac=0

k  

2

−4(2)(3)=0

k  

2

=24

k=±  

24

​  

=±2  

6

​  

 

ii)  

If kx  

2

−2kx+6=0 has equal roots, then b  

2

−4ac=0.

Here, a=k,b=−2k,c=6

kx(x−2)+6=0

kx  

2

−2kx+6=0

4k  

2

−4(k)(6)=0

4k  

2

−24k=0

4k(k−6)=0

For k=0, equation is not quadratic.

k=6