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A determinant containing a variable 
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#1
Jan1513, 01:50 PM

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1. The problem statement, all variables and given/known data
I have this 4x4 determinant and usually these are just mechanical work, until I stumbled upon one containing x, how should one go about solving these type of determinants? [x 2x 4 x ] [1 2 2x 1 ] [2x x1 2 3x] [ 2 x+1 x+3 x1] What are the different values of x? 2. Relevant equations 3. The attempt at a solution I've tried ellimination and by using cofactors. When fully computed, it will be a polynomial of the 4th degree, as one probably can see. Ellimination didn't make it simpler to factorize and cofactors just solved it until the polynomial popped up at the end 


#2
Jan1513, 01:52 PM

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#3
Jan1513, 02:04 PM

P: 25

8x^{4}22x^{3}22x^{2}+47x+3



#4
Jan1513, 09:52 PM

HW Helper
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PF Gold
P: 7,575

A determinant containing a variable
\left\begin{array}{cccc} x & 2x & 4 & x \\ 1 & 2 & 2x & 1\\ 2x & x1 & 2 & 3x\\ 2 & x+1 & x+3 & x1 \end{array}\right$$ If so, your last two terms should be ##44x+12##. Still, once you have the polynomial correct, you haven't said what you are supposed to do with it. It doesn't make sense to ask "what are the different values of ##x##". 


#5
Jan1613, 07:58 AM

Math
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PF Gold
P: 39,338




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