Hiya,

I need to find the range of values of k which give distinct roots, given the following 2 equations:

kx + y = 3

x^2 + y^2 = 5

Thanks guys.

Kermola

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- Dec 13th 2012, 03:46 AMkermolaSimultaneous Equation
Hiya,

I need to find the range of values of k which give distinct roots, given the following 2 equations:

kx + y = 3

x^2 + y^2 = 5

Thanks guys.

Kermola - Dec 13th 2012, 05:34 AMemakarovRe: Simultaneous Equation
Attachment 26201

The angles B and B' are 90°, but angle BAB' is not 90°. You can find $\displaystyle \cos(\angle AOB')$, from where you can find the slope of AB' (recall that $\displaystyle \tan(\alpha)\tan(\alpha+\pi/2)=-1$). - Dec 13th 2012, 05:37 AMkermolaRe: Simultaneous Equation
Thanks for that.

Any way to solve it without trigonometry and without drawing out the graphs? i.e. solve it algebraically?

Thanks - Dec 13th 2012, 05:46 AMemakarovRe: Simultaneous Equation
You can express y from the first equation and substitute it into the second one. You'll get a quadratic equation in x with coefficients depending on k. Determine for which k the discriminant is positive.

- Dec 13th 2012, 05:46 AMkermolaRe: Simultaneous Equation
Oh I've managed to figure it out!

Correct me if I'm wrong :

from (1) - y = 3 - kx

therefore x^2 + (3-kx)^2 = 5

x^2 + 9 - 6kx + 9 = 5

(k^2 + 1)x^2 - 6kx + 4 = 0

using b2 - 4ac to find real roots

(-6k)^2 - 16k^2 - 16 > 0

36k^2 - 16k^2 - 16 > 0

20k^2 > 16

k^2 > 4/5

-2/(5^(1/2)) < k > 2/(5^(1/2))

Hmm.. what program do people use to write proper it in proper mathematical form to post on these forums? That'd be helpful for the future.

Kermola - Dec 13th 2012, 05:51 AMemakarovRe: Simultaneous Equation
Ha-ha, I was early by 5 seconds!

The last line is incorrect.

See the LaTeX Help subforum. Wrap LaTeX code in [TEX]...[/TEX] tags. - Dec 13th 2012, 05:52 AMkermolaRe: Simultaneous Equation
I've since editted my post - we keep missing each other!

Thanks for the latex pointer - i'll check it out.

Is the editted post correct?

Thanks so much for help.

Kerm - Dec 13th 2012, 05:59 AMemakarovRe: Simultaneous Equation
- Dec 13th 2012, 08:17 AMkermolaRe: Simultaneous Equation
I was just being a bit lazy when I edited the post. Thanks a lot for the help!

K