anonymous
  • anonymous
Please explain how to find the value for k for which this equation has one repeated root x^2-2x+k=0
Algebra
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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IrishBoy123
  • IrishBoy123
why no start with seeing what it looks like to have a repeated root, say a? so multiply out \((x-a)^2\) and pattern match
anonymous
  • anonymous
(x-a)(x-a) x^2-ax-ax+a^2 I don't quite understand how this relates to the problem?
IrishBoy123
  • IrishBoy123
\(x^2-ax-ax+a^2 = \\ x^2 - 2ax + a^2\) original problem: \(x^2-2x+k=0\) geddit?

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anonymous
  • anonymous
Sorry, no I really don't. The two equations don't look similar to me because the original equation does not have two squared variables and the middle term doesn't have two variables.
IrishBoy123
  • IrishBoy123
pattern match
IrishBoy123
  • IrishBoy123
|dw:1439636560854:dw|
anonymous
  • anonymous
All right. But how does that fit in? must i make a variable 'a' and solve for that first or something?
anonymous
  • anonymous
For the simple ones like x^2-2x+k I can figure it out logically by using b^2-4ac=0. Then i get 4-4*1*k =0 and can easily go from there however I don't think this works for the more complicated ones unless I am doing it wrong? The most complicated one I have to do in this exercise is 3x^2 +2kx-3k
IrishBoy123
  • IrishBoy123
yes, you solve ! \(-2a = -2 \implies a = 1\) \(k = a^2 \implies k = ...\) but if you're happier with the \(b^2 - 4ac = 0\) approach, which is fine, do it for: \( 3x^2 +2kx-3k = 0\) repeated root \( \implies (2k)^2 - 4(3)(-3k) = 0 \implies k(4k+36) = 0\) k = 0 means \(3x^2 = 0\) k = -9 gives you the solution
IrishBoy123
  • IrishBoy123
typo: "k = -9 gives you the ***other*** solution"
anonymous
  • anonymous
Ok! That really helps! One little thing though, so does (2k)^2=4k^2 then?
IrishBoy123
  • IrishBoy123
\((2k)^2=4k^2\) \(\checkmark\)
anonymous
  • anonymous
Thank you very very much! That has helped me a lot!
anonymous
  • anonymous
solve for k. x^2−2x+k=0 Add -x^2 to both sides. x^2+k−2x+−x2=0+−x2 k−2x=−x^2 Add 2x to both sides. k−2x+2x=−x^2+2x k = −x^2+2x

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