Multiple choice

Determine the value of $k$ for which the quadratic equation $4x^2 - 3kx + 1 = 0$ has equal roots.

  1. $\displaystyle \pm \frac{2}{3} $
  2. $\displaystyle \pm \frac{4}{3} $
  3. $\displaystyle \pm 4$
  4. $\displaystyle \pm 6$
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B Correct answer
Explanation

For equal roots, the discriminant D = b^2 - 4ac = 0. Here (-3k)^2 - 4(4)(1) = 0, so 9k^2 = 16. Thus k^2 = 16/9, and k = +/- 4/3.

AI explanation

For a quadratic equation to have equal roots, its discriminant must be zero, so we equate the discriminant formula b squared minus 4ac to zero for the equation 4x squared minus 3kx plus 1 equals 0. Substituting the values gives negative 3k all squared minus 4 times 4 times 1 equals 0, which simplifies to 9k squared equals 16. Solving this yields k equals plus or minus 4 thirds.

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