document.write( "Question 1129801: If one root of the equation x^2 - mx + 2=0 is double the other, find the value of m. \n" ); document.write( "

Algebra.Com's Answer #746424 by math_helper(2461) $\"\"$ $\"About$

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let the roots be r and t, with r = 2t
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\n" ); document.write( "\n" ); document.write( "Then we can say:
\n" ); document.write( " $\"++r%5E2+-+mr+%2B+2+=+0+\"$ (1)
\n" ); document.write( " $\"++t%5E2+-+mt+%2B+2+=+0+\"$ (2)
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\n" ); document.write( "\n" ); document.write( "Substituting r=2t into (1):
\n" ); document.write( " $\"++4t%5E2+-+2mt+%2B+2+=+0+\"$
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\n" ); document.write( "\n" ); document.write( "This last equation and (2) can be solved for t in terms of m:
\n" ); document.write( "t = 3/m ( —> r = 6/m )
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\n" ); document.write( "\n" ); document.write( "Plugging in t = 3/m into (2):
\n" ); document.write( " $\"+%289%2Fm%5E2%29+-+m%283%2Fm%29+%2B+2+=+0+\"$
\n" ); document.write( " $\"++9%2Fm%5E2+=+1+\"$
\n" ); document.write( " $\"++m%5E2+=++9+\"$
\n" ); document.write( " m = +/- 3
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\n" ); document.write( "\n" ); document.write( "Both values of m work as solutions:
\n" ); document.write( "m=-3:
\n" ); document.write( " $\"+x%5E2+%2B+3x+%2B+2+=+0+\"$ —> $\"+%28x%2B1%29%28x%2B2%29+=+0+\"$ —> x = -1 and x = -2
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\n" ); document.write( "\n" ); document.write( "m=3:
\n" ); document.write( " $\"+x%5E2+-+3x+%2B+2+=+0+\"$ —> $\"+%28x-1%29%28x-2%29+=+0+\"$ —> x = 1 and x = 2

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