Multiple choice

$x\, =\, \displaystyle \frac{-k}{2}$ is a root of quadratic equation $2x^{2}\, +\, (k\, - \,6)\, x\, -\, 3k\, =\, 0$

  1. True

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

Substitute x = -k/2 into 2x^2 + (k-6)x - 3k. This gives 2(k^2/4) + (k-6)(-k/2) - 3k = k^2/2 - k^2/2 + 3k - 3k = 0. Since the result is 0, the statement is true.

AI explanation

Substitute x = -k/2 directly into the quadratic equation 2x^2 + (k - 6)x - 3k = 0. This gives the equation 2(-k/2)^2 + (k - 6)(-k/2) - 3k = 0, which simplifies to k^2/2 - k^2/2 + 3k - 3k = 0. Because the equation balances to 0 = 0 for any value of k, the statement is True.

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