Multiple choice

The product of the roots of equation $2{ m }^{ 2 }-8m=0$ is

  1. $4$
  2. $2$
  3. $0$
  4. $-8$
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C Correct answer
Explanation

For a quadratic equation ax^2 + bx + c = 0, the product of roots is c/a. Here, 2m^2 - 8m + 0 = 0, so c = 0. Product = 0/2 = 0.

AI explanation

To find the product of the roots using Vieta's formulas, the quadratic equation must be set to standard form. Moving the 8m to the other side gives 2m^2 - 8m = 0, which can be divided by 2 to yield m^2 - 4m = 0. For the equation m^2 - 4m + 0 = 0, the product of the roots is the constant term divided by the leading coefficient. Thus, the product of the roots is 0 divided by 1, which equals 0.

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