Multiple choice

If the product of roots of the equation $mx^2 + 6x+ (2m-1)=0$ is $-1$, then the value of $m$ is

  1. $\dfrac{1}{3}$
  2. $1$
  3. $3$
  4. $-1$
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A Correct answer
Explanation

For mx^2 + 6x + (2m-1) = 0, the product of roots is c/a = (2m-1)/m. Given product = -1, (2m-1)/m = -1 => 2m-1 = -m => 3m = 1 => m = 1/3.

AI explanation

Using Vieta's formulas for the quadratic equation mx^2 + 6x + (2m - 1) = 0, the product of the roots is given by the constant term divided by the leading coefficient, which is (2m - 1)/m. We are given that the product of the roots is -1, so we set up the equation (2m - 1)/m = -1. Multiplying both sides by m gives 2m - 1 = -m, and solving for m yields 3m = 1, so m = 1/3.

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