Question 328671
Use the discriminant, D.
{{{D=b^2-4ac}}}
When D=0, the quadratic has one real rational (double) root.
{{{(3/4)x^2+kx+27=0}}}
{{{D=k^2-4(3/4)(27)=0}}}
{{{k^2-81=0}}}
{{{k=0 +- 9}}}
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Both instances of k are shown in the graph (+9-Red,-9 Green).
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{{{graph(300,300,-14,14,-8,8,(3/4)x^2+9x+27,(3/4)x^2-9x+27)}}}