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
Hello, bondra!
In other words, the graph that parabola has two x-intercepts.Determine the values of $\displaystyle k$ if the graph $\displaystyle y\:=\:2x^2-2x+3k$
intersects the x-axis at two distinct points,
. . That is: .$\displaystyle 2x^2-2x + 3k \:=\:0$ has two real roots.
Quadratic Formula: .$\displaystyle x \;=\;\frac{2 \pm \sqrt{4 - 24k}}{4}$
There are two real roots if the discriminant is positive:
. . That is: .$\displaystyle 4 - 24k \:>\:0 \quad\Rightarrow\quad -24k \:>\:-4 \quad\Rightarrow\quad\boxed{ k \:<\:\frac{1}{6}}$