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Other Topics => Completely Off-Topic => Topic started by: whitehouses81680 on December 29, 2005, 03:04:17 pm

Title: Wow this is completely off topic...
Post by: whitehouses81680 on December 29, 2005, 03:04:17 pm
I NEED HELP!

does anyone know how to do this math problem:

22. Find all the values of k such that the expression 3x^2-2x+k=0 has imaginary roots.
Title: Wow this is completely off topic...
Post by: whitehouses81680 on December 29, 2005, 03:05:22 pm
I SHOULD HAVE POSTED THIS ON THE OTHER TOPIC...SRY
Title: Wow this is completely off topic...
Post by: LimeTwister on December 29, 2005, 04:05:16 pm
if i am thinking correctly you should use the square root of b squared minus (4)(a)(c).

which would give you all numbers k> -1 would be the answer....

EDIT:
uh, I didn't finish working out the problem... and Will actually finished. (obviously, I am not going to be a math major). So, look at Will's.
Title: Wow this is completely off topic...
Post by: Will on December 29, 2005, 04:50:43 pm
3*x^2 - 2*x + k = 0

f(x) = 3*x^2 - 2*x + k

As you recall, there exists a formula to find the roots of all quadratic equations in the form of a*x^2 + b*x + c = 0. The formula is,

x = (-b (+/-)(d)^(1/2)) / (2*a)

where d = b^2 - 4*a*c.

The only place in this formula that would give rise to an imaginary number (and hence, give us a solution with a non-zero imaginary component) is the radical, if and only if the quantity under it is negative. So, f(x) has roots with a non-zero imaginary component where d < 0 (d is negative). We are already given a and b. We'll plug those into the formula for d and substitute that into the inequality I stated above. Then, we'll solve for c, which is k in the original statement of the problem.

a = 3
b = -2
c = k

b^2 - 4*a*c < 0
4 - 4*3*k < 0
-12*k < -4
k > (1/3)

Therefore, f(x) has roots with a non-zero imaginary part where k > (1/3).
Title: Wow this is completely off topic...
Post by: LimeTwister on December 29, 2005, 04:55:09 pm
wouldn't that be 1/3?

where did you get 1/4?
Title: Wow this is completely off topic...
Post by: Will on December 29, 2005, 05:05:29 pm
Made a mistake. Fixed.
Title: Wow this is completely off topic...
Post by: LimeTwister on December 29, 2005, 05:08:53 pm
lol well, at least you finished working it out...i feel rather dumb...
Title: Wow this is completely off topic...
Post by: whitehouses81680 on December 29, 2005, 06:47:29 pm
WILL, LIMETWISTER, YOU ALL ROCK...thanks a bunch<3
Title: Wow this is completely off topic...
Post by: whitehouses81680 on December 29, 2005, 06:51:06 pm
and just to throw it out there if anyone is really bored:

The accompanying diagram shows a circular machine part that has rods PT and PAR attached at points T, A, and R which are located on teh circe: mTA:mAR:mRT-1:3:5; RA=12 centimeteres; and PA=5 centimeters

Find the measure of angle P in degrees and the find the length of rod PT to the nearest tenth of a centimeter....

i got that P= 80 degrees

i dont know how to find PT?
Title: Wow this is completely off topic...
Post by: Will on December 29, 2005, 08:45:27 pm
Ok... I was gonna do the problem, but I have a question. You said "mTA:mAR:mRT-1:3:5." I read that as a ratio of the three lengths (1:3:5). However, if I do that, mRT = 20 cm, mRA = 12 cm, and mTA = 4 cm. 12+4 = 16 < 20, so that isn't a triangle. Could you explain what you mean?
Title: Wow this is completely off topic...
Post by: whitehouses81680 on December 30, 2005, 09:34:19 am
mTA:mAR:mRT-1:3:5<--- thats a circle. The whole circle is broken up...


idk how i can get the diagram on the site  :(
Title: Wow this is completely off topic...
Post by: GeNuInEwAnNaBe69 on December 30, 2005, 09:36:36 am
Scan it.
Title: Wow this is completely off topic...
Post by: Will on December 30, 2005, 09:46:15 am
Quote from: "whitehouses81680"
mTA:mAR:mRT-1:3:5<--- thats a circle. The whole circle is broken up...


idk how i can get the diagram on the site  :(


So, mTA and the like denote arcs? The ratio of their lengths is 1:3:5?
Title: Wow this is completely off topic...
Post by: GeNuInEwAnNaBe69 on December 30, 2005, 10:47:44 am
the answer is 9.2 sam, but i don't know why
Title: Wow this is completely off topic...
Post by: whitehouses81680 on December 30, 2005, 06:25:21 pm
what math did u show?