Multiple choice

If the equation $\displaystyle 16x^{2}+6kx+4=0$ has equal roots, then the value of $k$ is

  1. $\displaystyle \pm 8$
  2. $\displaystyle \pm \frac{8}{3}$
  3. $\displaystyle \pm \frac{3}{8}$
  4. $0$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For equal roots, discriminant D = b^2 - 4ac = 0. (6k)^2 - 4(16)(4) = 0. 36k^2 - 256 = 0. k^2 = 256/36 = 64/9. k = +/- 8/3.

AI explanation

For a quadratic equation of the form ax^2 + bx + c = 0 to have equal roots, the discriminant (b^2 - 4ac) must equal zero. Substituting the values gives (6k)^2 - 4(16)(4) = 0, which simplifies to 36k^2 - 256 = 0. Solving for k^2 gives 64/9, so k equals +8/3 or -8/3.

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