Questions on Algebra: Quadratic Equation answered by real tutors!

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Question 155245: for what value(s) of k will the graph of y = x^2-3x+k
a) touch the x-axis
b) never meet the x-axis?: for what value(s) of k will the graph of y = x^2-3x+k
a) touch the x-axis
b) never meet the x-axis?
Answer by jim_thompson5910(9162) About Me  (Show Source):
You can put this solution on YOUR website!
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.



b)

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