Multiple choice

If one root of the quadratic equation $2x^2+kx-6=0$ is $2$, find the value of k. Also, find the other root.

  1. $k=-1$   and   the other root is $=\dfrac{3}{2}$
  2. $k=1$   and   the other root is $=\dfrac{-3}{2}$
  3. $k=1$   and   the other root is $=\dfrac{3}{2}$
  4. $k=-1$   and   the other root is $=\dfrac{-3}{2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If x=2 is a root, then 2(2^2) + k(2) - 6 = 0, so 8 + 2k - 6 = 0, which means 2k = -2, so k = -1. The equation becomes 2x^2 - x - 6 = 0. Factoring: (2x + 3)(x - 2) = 0. The roots are 2 and -3/2.

AI explanation

Since 2 is a root of 2x^2 + kx - 6 = 0, substituting x = 2 yields 2(4) + 2k - 6 = 0, which simplifies to 2k = -2 so k = -1. Using Vieta's formula for the product of roots, the product of 2 and the other root equals -6/2 = -3, meaning the other root is -3/2. Therefore, k = -1 and the other root is -3/2.

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