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**Noilemaillilm** · 03-14-2008, 07:20 PM

Given the equation x^2+kx+1=0 and x^2-x +k=0 has common roots, find the values of k and the common roots.

Somebody asked me for help on this question but I'm kinda stumped as well. Anyway here's what I came up with, I have a feeling that I'm wrong though.

Code:

Code

x^2 + kx + 1 = 0  b^2 - 4ac = 0  k^2 - 4 (1)(1) k^2 = 4 k = 2  x^2 + 2x + 1 = 0                          (x+1) (x+1) = 0                                                                                                                      x = -1  ----------------------------------------------------  X^2 - x + k = 0  b^2 - 4ac = 0  (-1)^2 - 4(1)(k) 1 - 4k = 0 -4k = -1 k = 1/4  x^2 - x + 1/4 [ -b +/- sqrt b^2 - 4ac ] / 2a [ -(-1) +/- sqrt (-1)^2 - 4(1)(1/4) ] / 2(1) 1 +/- 0 / 2 x = 1/2

Is my answer correct?

03-14-2008, 07:20 PM	#1
Noilemaillilm Join Date Nov 2005 Posts 443 Senior Member	Maths Help Given the equation x^2+kx+1=0 and x^2-x +k=0 has common roots, find the values of k and the common roots. Somebody asked me for help on this question but I'm kinda stumped as well. Anyway here's what I came up with, I have a feeling that I'm wrong though. Code: Code x^2 + kx + 1 = 0 b^2 - 4ac = 0 k^2 - 4 (1)(1) k^2 = 4 k = 2 x^2 + 2x + 1 = 0 (x+1) (x+1) = 0 x = -1 ---------------------------------------------------- X^2 - x + k = 0 b^2 - 4ac = 0 (-1)^2 - 4(1)(k) 1 - 4k = 0 -4k = -1 k = 1/4 x^2 - x + 1/4 [ -b +/- sqrt b^2 - 4ac ] / 2a [ -(-1) +/- sqrt (-1)^2 - 4(1)(1/4) ] / 2(1) 1 +/- 0 / 2 x = 1/2 Is my answer correct?
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