Question 943236
A discriminant question.  First derive the equation for the intersection, and solve for the x coordinate, which will be a formula including k.


{{{kx^2-5x+2=-3x+4}}}, simply through equating the expressions for y.
{{{kx^2-2x-2=0}}}
{{{x=(2+- sqrt(4+4k*2))/(2k)}}}----solution for general quadratic equation applied
{{{x=(2+- sqrt(4(1+2k)))/(2k)}}}
{{{x=(2+- 2*sqrt(1+2k))/(2k)}}}
{{{highlight(x=(1+- sqrt(1+2k))/k)}}}


Now use what you are supposed to know about the discriminant to find your answers for k, and be aware, {{{k<>0}}}.