Multiple choice

For which value of $k$ will the equations ${x}^{2}-kx-21=0$ and ${x}^{2}-3kx+35=0$ have one common root.

  1. $\pm 1$
  2. $\pm 2$
  3. $\pm 4$

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If the equations have a common root 'a', then a^2 - ka - 21 = 0 and a^2 - 3ka + 35 = 0. Subtracting the two equations gives 2ka - 56 = 0, so ka = 28. Substituting ka = 28 into the first equation gives a^2 - 28 - 21 = 0, so a^2 = 49, meaning a = 7 or -7. If a = 7, then 7k = 28, so k = 4. If a = -7, then -7k = 28, so k = -4.

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