Multiple choice

The roots of the quadratic equation $3x^2 - kx + 14 = 0$ are in the ratio $7 : 6$, then $k$ equals _________.

  1. $13$
  2. $12$
  3. $1$
  4. $-3$
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A Correct answer
Explanation

Let roots be 7a and 6a. Sum of roots = 13a = k/3. Product of roots = 42a^2 = 14/3. a^2 = 14/(3 * 42) = 1/9. a = 1/3. k = 3 * 13 * (1/3) = 13.

AI explanation

Let the roots be 7y and 6y. Using the product of roots formula for 3x^2 - kx + 14 = 0, we have 14 divided by 3 equals 42y^2, which gives y = 1 divided by 3. Using the sum of roots formula, k divided by 3 equals 13y, so substituting y gives k divided by 3 equals 13 divided by 3. Therefore, the value of k is 13.

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