Multiple choice

If the roots of the quadratic equation $3{x}^{2}-12x+m=0$ are equal, then the value of $m$ will be:

  1. $4$
  2. $7$
  3. $9$
  4. $12$
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D Correct answer
Explanation

For equal roots, the discriminant b^2 - 4ac must be zero. Here, (-12)^2 - 4(3)(m) = 0, so 144 - 12m = 0, which means m = 12.

AI explanation

For a quadratic equation to have equal roots, its discriminant must be zero, so we set b^2 - 4ac = 0. Substituting the values from the equation 3x^2 - 12x + m = 0 gives (-12)^2 - 4(3)(m) = 0. This simplifies to 144 - 12m = 0, meaning m = 12.

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