Multiple choice

If x = 2 is one of the roots of the quadratic equation kx2 - (k + 2)x + 2 = 0, find the value of k.

  1. -2

  2. -1

  3. 0

  4. 1

  5. 2
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D Correct answer
Explanation

If x=2 is a root, then k(2)^2 - (k+2)(2) + 2 = 0. 4k - 2k - 4 + 2 = 0. 2k - 2 = 0. k = 1.

AI explanation

Substitute x equals 2 directly into the given quadratic equation to find k. This yields k times 2 squared minus the quantity k plus 2 times 2 plus 2 equals 0, which simplifies to 4 k minus 2 k minus 4 plus 2 equals 0. Combining like terms gives 2 k minus 2 equals 0, so k equals 1.

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