Multiple choice

If the roots of a quadratic equation $2x^2+5x+3k=0$ is reciprocal to other then find the values of k.

  1. $k=\dfrac{3}{2}$
  2. $k=-\dfrac{3}{2}$
  3. $k=-\dfrac{2}{3}$
  4. $k=\dfrac{2}{3}$
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D Correct answer
Explanation

For roots to be reciprocals, the product of roots (c/a) must be 1. Here, 3k/2 = 1, so k = 2/3.

AI explanation

For a quadratic equation ax^2 + bx + c = 0, the product of the roots is given by c/a. If the roots are reciprocal to each other, their product must equal 1. Therefore, we write the equation 3k / 2 = 1. Solving this linear equation yields k = 2/3.

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