Multiple choice

Find the values of $\lambda$ so that the equations $x^2-\lambda x -21=0$ and $x^2-3\lambda x +35=0$ may have one common root.

  1. $\pm 1$
  2. $\pm 2$
  3. $\pm 3$
  4. $\pm 4$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For common root alpha, alpha^2 - lambda*alpha - 21 = 0 and alpha^2 - 3*lambda*alpha + 35 = 0. Subtracting: 2*lambda*alpha - 56 = 0 => lambda*alpha = 28. Substituting into first: alpha^2 - 28 - 21 = 0 => alpha^2 = 49 => alpha = +/- 7. If alpha = 7, lambda = 4. If alpha = -7, lambda = -4.

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