Question 1193921
<pre>

{{{y = (3k-1) x^2 - 6 x + 1}}}

has positive concavity when its graph, a parabola, opens upward, 
which is when the coefficient of x<sup>2</sup> is positive, which means 
greater than 0, so solve the inequality for k:

{{{3k-1>0}}}

Also to pass through the x-axis twice, its discriminant must 
be positive to give it two unique real zeros.  So simplify 
and solve this inequality for k:

{{{b^2-4ac>0}}}
{{{(-6)^2-4(3k-1)(1)>0}}}

Now look at the two solutions to those two inequalities and 
fill in fractions in the two blanks. 

___ < k < ___

Edwin</pre>