Question 94574
Find k such that the equation x(2)^-kx+4=0 has a repeated real solution. 
The discriminant tells you.
If b^2-4ac = 0 there will be two equal Real Number solutions.
Your Problem:
a=1,b=-k,c=4
b^2-4ac = (-k)^2-4*1*4 =k^2-16
k^2-16  0 
(k-4)(k+4) >0
True when k=4 and when k=-4
Conclusion: You will have two  equal Real Number solutions when
k=4 and when k=-4.
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Cheers,
Stan H.