For what value of k does the parabola y= x2/3 −kx+3 intersect the x-axis in only one point?

Answer 1

y = ( x^2) / 3 - k x + 3 ????
solution to quadratic is if y = a x^2 + b x + c
y= 0 (hits x axis) when x = [-a +/- sqrt(b^2-4ac) ]/ 2a
only one solution if b^2 - 4 a c = 0
so
b^2-4 a c = 0
k^2 - 4 = 0
k^2 = 2 or -2

Answer 2

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