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

 Aug 12, 2024
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ONE real root ( actually a double root) would mean the discrimination (from the Quadratic Formula) would be = 0 

b^2 - 4ac = 0        

X^2 + 4m x + m = 2x-6 

x^2 - (4m - 2) x + (m+6) = 0          A = 1      B = 4m-2     C = m+6 

(4m-2)^2 - 4 (1)(m+6) = 0 

16 m^2 -16m +4  - 4m - 24 = 0 

16 m^2 - 20m - 20 = 0          Now use quadratic formula    To find   M = 1.90587

 Aug 12, 2024

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