Problem

16. For what values of $m$ does the quadratic equation $(5 m-3) x^{2}-$ $4 m x+m+1=0$ have only one root?

Solution

Step 1 :Let's calculate the discriminant and set it equal to 0: \(D = b^2 - 4ac = (-4m)^2 - 4(5m - 3)(m + 1)\)

Step 2 :Setting the discriminant equal to 0: \(16m^2 - (m + 1)(20m - 12) = 0\)

Step 3 :Solving for m, we get two values: \(m = -3\) and \(m = 1\)

Step 4 :\(\boxed{m = -3, m = 1}\)

From Solvely APP
Source: https://solvelyapp.com/problems/8389/

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