Answer:
[tex]\boxed{\sf k=6}[/tex]
Step-by-step explanation:
[tex]\sf kx (x-2)+6=0[/tex]
Expand brackets.
[tex]\sf kx^2 -2kx+6=0[/tex]
This is in quadratic form.
[tex]\sf ax^2 +bx+c=0[/tex]
Since this is for equal roots:
[tex]\sf b^2 -4ac=0[/tex]
[tex]\sf a=k\\b=-2k\\c=6[/tex]
[tex]\sf (-2k)^2 -4(k)(6)=0[/tex]
[tex]\sf 4k^2-24k=0[/tex]
[tex]\sf 4k(k-6)=0[/tex]
[tex]\sf 4k=0\\k=0[/tex]
[tex]\sf k-6=0\\k=6[/tex]
Plug k as 0 to check.
[tex]\sf \sf 0x^2 -2(0)x+6=0\\6=0[/tex]
False.
So that means k must equal 6.
