Multiple choice

If one root of the equation $2x^2-ax+64=0$ is twice the other, then find the value of a.

  1. $a= \pm 24$
  2. $a= \pm 4$
  3. $a= \pm 2$

  4. None of these
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A Correct answer
Explanation

Let roots be k and 2k. Sum of roots = 3k = a/2, so k = a/6. Product of roots = 2k^2 = 64/2 = 32, so k^2 = 16, k = +/- 4. If k = 4, a = 24. If k = -4, a = -24.

AI explanation

Let the roots be r and 2r. Using the product of roots formula, (r)(2r) = 64/2, which gives 2r^2 = 32 and r = 4. The roots are 4 and 8, or -4 and -8. Using the sum of roots formula, a/2 equals 4 + 8 or -4 + (-8), so a/2 is 12 or -12, making a = 24 or -24. The result is a = plus or minus 24.

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