Multiple choice

For what value of k the equation 3x2 – 2x + k = 0 have equal roots?

  1. -3

  2. 1/3

  3. 3

  4. More than one of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For a quadratic equation ax^2 + bx + c = 0 to have equal roots, the discriminant D = b^2 - 4ac must be 0. Here, (-2)^2 - 4(3)(k) = 0, so 4 - 12k = 0, which means 12k = 4, so k = 1/3.

AI explanation

For a quadratic equation to have equal roots, its discriminant (b squared minus 4ac) must equal zero. Substituting the values from the equation 3x squared minus 2x plus k equals 0 gives the equation (negative 2) squared minus 4(3)(k) equals 0. Solving 4 minus 12k equals 0 yields k equals one-third.

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