Multiple choice

If one root of the quadratic equation $x^{2}\, -\, 10x\, +\, 2k\, =\, 0$ is $5\, -\, \sqrt3,$ find $k$.

  1. $11$
  2. $12$
  3. $13$
  4. $15$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If one root is 5 - sqrt(3), the other must be 5 + sqrt(3) because the coefficients are rational. The sum of roots is 10, which matches the equation x^2 - 10x + 2k = 0. The product of roots is (5 - sqrt(3))(5 + sqrt(3)) = 25 - 3 = 22. Since the product is 2k, 2k = 22, so k = 11.