Multiple choice

A quadratic equation whose one root is 3 + 2i is:

  1. x2 + 6x + 13 = 0

  2. x2 - 6x - 13 = 0

  3. x2 - 6x + 13 = 0

  4. 2x2 - 6x + 13 = 0
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If roots are 3 + 2i and 3 - 2i, the sum of roots = 6 and product = 3^2 + 2^2 = 13. The equation is x^2 - (sum)x + (product) = 0, which is x^2 - 6x + 13 = 0.

AI explanation

For a quadratic equation with real coefficients, complex roots must be complex conjugates, so the second root is 3 - 2i. The required equation is found using x^2 - (sum of roots)x + (product of roots) = 0. The sum of the roots is (3 + 2i) + (3 - 2i) = 6, and the product of the roots is (3 + 2i)(3 - 2i) = 9 - (4i^2) = 9 + 4 = 13. Substituting these values gives the equation x^2 - 6x + 13 = 0.

Keep practicing — related questions