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)

1 answer

intersect the line with the parabola

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

Looks like you are studying the nature of the roots, remember that if
b^2 - 4ac > 0 you will have two solutions
b^2 - 4ac = 0 you will have 1 solution (2 equal ones)
b^2 - 4ac < 0 , there is no solution

so apply those conditions for each of your questions
Let me know what you get