x^2+y^2=2a+4

x+y=a+3

find the meaning for "a" when system of equation has only 1 root

please someone help. thanks

(sorry for bad english)

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- Jun 13th 2012, 04:07 PMTeloParametric system of equation problem
x^2+y^2=2a+4

x+y=a+3

find the meaning for "a" when system of equation has only 1 root

please someone help. thanks

(sorry for bad english) - Jun 13th 2012, 04:27 PMPlatoRe: Parametric system of equation problem
- Jun 13th 2012, 04:34 PMTeloRe: Parametric system of equation problem
thanks for answer but i didnt get it, i have this: 2x^2-2ax+a^2+9=2a+4 what do i do next? how do i find out what meaning must "a" have? for 1 root of x

- Jun 13th 2012, 04:51 PMHallsofIvyRe: Parametric system of equation problem
Do you not know how to solve a quadratic equation?

But more to the point, that equation can be written Now, an equation like that will have only one root provided it is a**double**root. That is, if it is of the form . - Jun 14th 2012, 12:22 AMrichard1234Re: Parametric system of equation problem
Expanding on HallsofIvy's post, you have a double root if and only if the discriminant is zero, i.e.

Solve the quadratic. - Jun 14th 2012, 02:53 AMTeloRe: Parametric system of equation problem
thank you very much! I've got a=-1

- Jun 14th 2012, 08:35 AMrichard1234Re: Parametric system of equation problem
Hmm I'm not sure if -1 is correct...according to the quadratic I posted, it has two non-real roots for a.

- Jun 14th 2012, 09:29 AMReckonerRe: Parametric system of equation problem
-1 should be correct. I get a single solution for the resulting system.

My work disagrees slightly with HallsofIvy, however:

For this quadratic to have a single root, the discriminant must be 0:

Substituting this back into the original equations gives the system

So

A single solution, as desired.