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

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- Nov 25th 2008, 07:56 AMbondrax 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 - Nov 25th 2008, 08:08 AMSoroban
Hello, bondra!

Quote:

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