Multiple choice

The value of k for which the roots are real and equal of the following equation $2x^2$ + kx + 3 = 0 is k = $\pm2\sqrt6$

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For 2x^2 + kx + 3 = 0, D = k^2 - 4(2)(3) = k^2 - 24. For real and equal roots, D=0, so k^2 = 24, k = +/- sqrt(24) = +/- 2*sqrt(6).

AI explanation

For the roots to be real and equal, the discriminant b^2 - 4ac must equal zero. Substituting the coefficients gives k^2 - 4(2)(3) = 0, which simplifies to k^2 - 24 = 0. Solving this yields k = sqrt(24), which simplifies to k = plus or minus 2*sqrt(6); the statement is true.

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