SOLUTION: If one root of the equation x^2 - mx + 2=0 is double the other, find the value of m.

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Question 1129801: If one root of the equation x^2 - mx + 2=0 is double the other, find the value of m.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
let the roots be r and t, with r = 2t

Then we can say:
++r%5E2+-+mr+%2B+2+=+0+ (1)
++t%5E2+-+mt+%2B+2+=+0+ (2)

Substituting r=2t into (1):
++4t%5E2+-+2mt+%2B+2+=+0+

This last equation and (2) can be solved for t in terms of m:
t = 3/m ( —> r = 6/m )

Plugging in t = 3/m into (2):
+%289%2Fm%5E2%29+-+m%283%2Fm%29+%2B+2+=+0+
++9%2Fm%5E2+=+1+
++m%5E2+=++9+
m = +/- 3

Both values of m work as solutions:
m=-3:
+x%5E2+%2B+3x+%2B+2+=+0+ —> +%28x%2B1%29%28x%2B2%29+=+0+ —> x = -1 and x = -2

m=3:
+x%5E2+-+3x+%2B+2+=+0+ —> +%28x-1%29%28x-2%29+=+0+ —> x = 1 and x = 2