Multiple choice

The values of k for which the roots are real and equal of the following equation $3x^2$ - 5x + 2k = 0 is k = $\dfrac{25}{24}$

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For 3x^2 - 5x + 2k = 0 to have equal roots, discriminant D = b^2 - 4ac = 0. (-5)^2 - 4(3)(2k) = 0. 25 - 24k = 0, so k = 25/24.

AI explanation

The condition for a quadratic equation to have real and equal roots is that its discriminant (b^2 - 4ac) equals zero. For the equation 3x^2 - 5x + 2k = 0, we have a = 3, b = -5, and c = 2k. Setting the discriminant to zero gives (-5)^2 - 4(3)(2k) = 0, which simplifies to 25 - 24k = 0. Solving this gives k = 25/24, making the statement True.

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