Multiple choice

Find k if one root of the equation $ \displaystyle x^{2}-6kx+8=0 $ is twice the other

  1. $2$
  2. $ \displaystyle \pm 1 $
  3. $ \displaystyle \pm \frac{1}{2}$
  4. $3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let roots be a and 2a. Sum of roots = 3a = 6k, so a = 2k. Product of roots = 2a^2 = 8, so a^2 = 4, a = +/- 2. If a = 2, 2k = 2, k = 1. If a = -2, 2k = -2, k = -1. Thus k = +/- 1.

AI explanation

Let the roots be r and 2r. By Vieta's formulas, the sum of the roots is r + 2r = 6k, and the product is r times 2r = 8. From the product equation, 2r^2 = 8, which gives r^2 = 4 and r = 2 or -2. Substituting these into the sum equation gives 3(2) = 6k or 3(-2) = 6k, both of which result in k = 1 or k = -1. Therefore, k equals plus or minus 1.

Keep practicing — related questions