Question 119661
If 1 is a root, then {{{f(1)=0}}}. 


{{{(3k+1)x^2-2kx=-5}}} Start with the given equation



{{{(3k+1)x^2-2kx+5=0}}} Add 5 to both sides



{{{(3k+1)(1)^2-2k(1)+5=0}}} Plug in {{{x=1}}}



{{{3k+1-2k+5=0}}} Simplify



{{{k+6=0}}} Combine like terms on the left side



{{{k=-6}}}Subtract 6 from both sides


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Answer:

So our answer is {{{k=-6}}}