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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?

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  • $\begingroup$ @Gal that simply isn't true. $\endgroup$ – Frank Apr 1 '14 at 19:38
  • $\begingroup$ Yeah sorry i realized i made a mistake. Solved it like you but assumed something that isn't true. $\endgroup$ – Gal Apr 1 '14 at 19:42
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Set the two RHS's equal to each other: $3x +k = 2x^2 - 5x+3$.

Rearrange: $2x^2 - 8x +(3-k) = 0.$

There is precisely one intersection if and only if the descriminant of this quadratic equals zero.

The descriminant is $64 -8(3-k) = 40 + 8k $, and this equals zero if and only if $k=-5$.

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  • $\begingroup$ Oh thanks a lot. I forgot about the discriminant. I understand how to do it now. $\endgroup$ – Oscar Apr 1 '14 at 19:37
  • $\begingroup$ OK, that's a pleasure. If you are satisfied with the answer, don't forget that it's possible to accept it :) $\endgroup$ – Frank Apr 1 '14 at 19:38

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