# Math Help - x intersection

1. ## x intersection

Determine the values of "k" if the graph y=2x^2-2x+3k intersects the x-axis at two distinct points,
help would be cool

2. Hello, bondra!

Determine the values of $k$ if the graph $y\:=\:2x^2-2x+3k$
intersects the x-axis at two distinct points,
In other words, the graph that parabola has two x-intercepts.

. . That is: . $2x^2-2x + 3k \:=\:0$ has two real roots.

Quadratic Formula: . $x \;=\;\frac{2 \pm \sqrt{4 - 24k}}{4}$

There are two real roots if the discriminant is positive:

. . That is: . $4 - 24k \:>\:0 \quad\Rightarrow\quad -24k \:>\:-4 \quad\Rightarrow\quad\boxed{ k \:<\:\frac{1}{6}}$