Question

Find the value of k such that the equation of the tangent line to f(x) = x^2 + k*x is equal to y = 5*x + 3

Answer 1

@ganeshie8

Answer 2

\(x^2+kx =5x+3 \implies x^2+x(k-5)-3=0 \)
Notice that the discriminant is always \(\ge 12\), therefore \(y=5x+3\) cannot be a tangent

Answer 3

lol
I found the tangent line at (a,f(a)) since this was not given...;
The tangent line was:
\[y=(2x+k)x-a^2 \\ \\ -a^2 \neq 3\]

Answer 4

@ganeshie8 can you explain the part about the discriminant \(\ge 12\)?

Answer 5

mistype for me

Answer 6

\[y=(2\color{red}a+k)x-a^2\]

Answer 7

Ahh nice, \(-a^2\ne 3\) for any real \(a\) so no solutions..

Answer 8

@Jhannybean

basically we get tangent line only if below system has a single solution :
```
y = x^2+kx
y = 5x+3
```

Answer 9

that's true
for that line to be tangent at some point on the curve that tangent line and curve thing will have to share a common point

Answer 10

In other words, we want both the line and parabola to intersect at just one point

since the parabola opens up, the above system must have exactly one solution for tangent line

Answer 11

it is easy see from the graph that the tangent lien cannot cut the parabola back, at a different place..

Answer 12

Yeah,the explanation and the graph makes sense, i was just wondering where the 12 came from.

Answer 13

I can't believe this was posted a year ago... I guess we will never be able to ask the asker for any corrections to his problem.

Answer 14

```
y = x^2+kx
y = 5x+3
```

set the right hand sides equal to each other, you get a quadratic
the discriminant of the quadratic must have to be 0, but it happens that \(D\ge 12\)
so no such tangent

Answer 15

OHHH.... thats what i was missing haha, i get it now!

Answer 16

wow! it was posted one year ago... must be tha the OP has accidentally bumped it..

Answer 17

Maybe they were STILL working on the same problem.....from a year ago!

Answer 18

I don't know... Everything thing he has done was over a year ago. There has not been any other activity in posting answers or questions since a year.

Answer 19

According to the profile.

Answer 20

@medisynergi22