# Intersection of linear and quadratic functions

I've been stuck on some math work and I'm not sure how to do it. It involves finding the point where a quadratic and linear function intersect only once.

Determine the value of $k$ such that $g(x) = 3x+k$ intersects the quadratic function $f(x) = 2x^2 -5x +3$ at exactly one point.

How do I figure out the $k$ value?

• @Gal that simply isn't true. – Frank Apr 1 '14 at 19:38
• Yeah sorry i realized i made a mistake. Solved it like you but assumed something that isn't true. – Gal Apr 1 '14 at 19:42

Set the two RHS's equal to each other: $3x +k = 2x^2 - 5x+3$.
Rearrange: $2x^2 - 8x +(3-k) = 0.$
The descriminant is $64 -8(3-k) = 40 + 8k$, and this equals zero if and only if $k=-5$.