Question 155245
a) 


It will touch the x-axis when the polynomial has only one solution. If the polynomial has only one solution, then the discriminant is equal to zero. 



{{{D=b^2-4ac}}} Start with the discriminant formula



{{{0=(-3)^2-4(1)(k)}}} Plug in {{{D=0}}}, {{{a=1}}}, {{{b=-3}}} and {{{c=k}}}



{{{0=9-4(1)(k)}}} Square -3 to get 9



{{{0=9-4k}}} Multiply



{{{-9=-4k}}} Subtract 9 from both sides



{{{9/4=k}}} Divide both sides by -4



So when {{{k=9/4}}}, then the polynomial will have only one solution and will touch the x-axis.


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b)


Follow the same procedure described above, but this time {{{D<0}}}.