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The quadratic equation $x^2+4mx+m = 2x - 6$ has exactly one real root. Find the positive value of $m$.

 May 14, 2024
 #1
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Rearrange as

 

x^2 + (4m - 2)x + (m + 6)   =  0

 

If one root, the discriminant =   0

 

(4m - 2)^2  - 4(1)(m + 6) =   0

 

16m^2 - 16m + 4 - 4m - 24 =   0

 

16m^2 - 20m - 20 = 0

 

4m^2 - 5m - 5 =  0

 

m =  [ 5 + sqrt [ 25 + 80] ] / 8  =    5/8  + sqrt (105) / 8

 

cool cool cool

 May 14, 2024

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