Multiple choice

In the equation $2x^2 - hx + 2k = 0$, the sum of the roots is 4 and the product of the roots is -3. Then h and k have the values, respectively:

  1. 8 and -6

  2. 4 and -3

  3. -3 and 4

  4. -3 and 8

  5. 8 and -3
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E Correct answer
Explanation

For ax^2 + bx + c = 0, sum of roots = -b/a and product of roots = c/a. Here, 2x^2 - hx + 2k = 0. Sum = h/2 = 4, so h = 8. Product = 2k/2 = k = -3. Thus h=8, k=-3.

AI explanation

For the quadratic equation 2x^2 - hx + 2k = 0, Vieta's formulas state that the sum of the roots is h/2 and the product of the roots is 2k/2 = k. Equating these to the given values, we have h/2 = 4 and k = -3. Solving for h gives h = 8. Therefore, the values of h and k are 8 and -3 respectively.

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