Multiple choice

If one root of the equations x2 + 2x + 3k = 0 and 2x2 + 3x + 5k = 0 is common then the value of k is

  1. 1, 2

  2. 0, –1

  3. 1, 3

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If x is a common root, x^2 + 2x + 3k = 0 and 2x^2 + 3x + 5k = 0. Multiply the first by 2: 2x^2 + 4x + 6k = 0. Subtract the second: (2x^2 + 4x + 6k) - (2x^2 + 3x + 5k) = 0 => x + k = 0, so x = -k. Substitute x = -k into the first: (-k)^2 + 2(-k) + 3k = 0 => k^2 + k = 0 => k(k+1) = 0. Thus k = 0 or k = -1.

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