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)

Here's my work on it:
kx^2-5x+2=-3x+4
kx^2-2x-2=0

a)b^2-4ac
(-2^2-4(1)(-2)
(-4--8)
(4)

Can you please help me with b & c and tell me where I went wrong with a) if I did so. Thanks!

Answer 1

the discriminant is

25 - 8k

so, for one (repeated) root, 25-8k=0

find that, and then any value of k greater will produce a negative discriminant

any lesser value of k will produce a positive discriminant.