If 2+3i is one of the roots of the equation 2x^3 – 9x^2 + kx – 13 = 0

• Complex Numbers

If 2+3i is one of the roots of the equation 2x³ – 9x² + kx – 13 = 0, k ∈ R, then the real root of this equation:

1. does not exist
2. exists and is equal to 1/2
3. exists and is equal to -1/2
4. exists and is equal to 1

Solution

If one root is 2+3i, then second root must be 2-3i. Let α be the real root.

Sum of roots = 9/2

2 + 3i + 2 – 3i + α = 9/2

α = 1/2

The correct option is B.