Multiple choice

If the equations x2 - kx - 21 = 0 and x2 - 3kx + 35 = 0 have a common root, then the value of k is equal to

    • 4

  2. 4 or - 4

  3. 5 or 4

  4. 6
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let alpha be the common root. alpha^2 - k*alpha - 21 = 0 and alpha^2 - 3k*alpha + 35 = 0. Subtracting: 2k*alpha - 56 = 0, so k*alpha = 28, alpha = 28/k. Substitute into first: (28/k)^2 - k(28/k) - 21 = 0. 784/k^2 - 28 - 21 = 0. 784/k^2 = 49. k^2 = 784/49 = 16. k = 4 or -4.

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