Question

If the system y=x^2+2x+3 and y=kx-1 has exactly one solution, then what does k equal?

Answer 1

\[y = x^{2} + 2x + 3\]
\[y = kx - 1\]
Since they have one solution, set the equal to each other..
\[x^{2} + 2x + 3 = kx - 1\]

Answer 2

Will K have a value in this instance or will it be: k = x+2+4/x ?

Answer 3

\[x^{2} - (k - 2)x + 4 = 0\]
\[x^{2} - 4x + 4 = 0\]
The second one gives 1 solution. Do you see what K should be?

Answer 4

I understand how you got the first equation but not sure how you got to the second one.

Answer 5

That one has no correlation with the first equation, it is there because it has one solution and has the same format as the first one (x^2 ... -4)

Answer 6

Ah I think I understand, just bear with me, K should be 2?

Answer 7

Not quite
Type out what is the ONLY difference between the 2 equations and post it here

Answer 8

Okay,(k-2)x and (4x)

Answer 9

Now, take out the x and what do you have?

Answer 10

k-2 and 4

Answer 11

Right, now set these 2 equal and see what you get.

Answer 12

K=6 so when you multiply out (6-2)x it equals 4x so the equations will be the same, I got it! I think..

Answer 13

Just put your formula into quadratic form, and find the number that will be the 1 solution, for example (x - 2)^2, (x - 3)^2, etc.
You got this one!

Answer 14

Are you still confused on the 2nd step? I know it can be a little confusing..

Answer 15

I understand everything except for how you got x^2−4x+4=0

Answer 16

Ok, well in order for an equation to have 1 solution, it must be like (x-2)^2, (x-3)^2, etc.
Expand (x-2)^2 and tell me what you get.

Answer 17

x^2-4x+4

Answer 18

So, you see where I got the equation now?

Answer 19

Yeah, I got it. So is the final answer for what does K equal 6?

Answer 20

Yes!

Answer 21

Thanks! Can you help me with one more problem? I'll post it now.

Answer 22

Yeah sure!