Question

Determine the value of k in y=kx^2-5x+2 that will result in the intersection of the line y=-3x+4 with the quadratic at
a) two points (1 mark)
b) one points (1 mark)
c) no point (1 mark)

Answer 1

you have the line intersecting when

kx^2-5x+2 = -3x+4
kx^2-2x-2 = 0

Now recall the discriminant, d=b^2-4ac
If d>0 there are two roots
If d=0, there is one root
If d<0 there are no real roots.

The discriminant of your equation is

4+8k

I expect you can determine when that is negative, zero, or positive.