Multiple choice

One root of Quadratic ${ 4x }^{ 2 }-8kx-9$ is negative of the other so the value of $ k$ is

  1. 0
  2. $\dfrac { 9 }{ 8 } $
  3. $-\dfrac { 9 }{ 8 } $
  4. $\dfrac { 9 }{ 4 } $
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A Correct answer
Explanation

If roots are alpha and -alpha, their sum is 0. Sum of roots = -(-8k)/4 = 2k. 2k = 0, so k = 0.

AI explanation

The equation provided is 4x^2 - 8kx - 9 = 0. If one root is the negative of the other, let the roots be r and -r. The sum of these roots is r + (-r) = 0. Using Vieta's formulas, the sum of the roots of the quadratic ax^2 + bx + c = 0 is given by -b/a. Here, the sum of the roots is -(-8k) / 4 = 2k. Setting the sum equal to zero gives 2k = 0, which means k = 0.

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