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?

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Step:1 ：Let&#x27;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})

Answer

Step: 1 ：Let&#x27;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})

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?

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