How would i determine the values of 'k' if the graph y=2x^2-2x+3k intersects the x-axis at two distinct points?

Answer 1

This is similar ot the other problem.

If the equation crosses the x-axis then y=0.

So you need to find the solutions for

0=2x^2-2x+3k

using the general equation we get

x=-2+/-(4-4.2.3k)^.5/4

for there to be real values

4-24k>0 (we can't square root a number less than zero, and it can't equal zero as the question says there are two distinct points. Zero would give us two coincident points)

so 4>24k or k<4/24 k<0.1667

Check my working!