JEE Main 2015 · 10 Apr · Shift 1 · Mathematics Q63

MathematicsSingle correct+4 / -1Question 63 of 90

If $2+3i$ is one of the roots of the equation $2x^3-9x^2+kx-13=0$ , $k\in\mathbb R$ , then the real root of this equation :

does not exist.

exists and is equal to

\dfrac12

exists and is equal to

-\dfrac12

exists and is equal to 1.

Answer and worked solution

Official answer: B

The real coefficients mean $2-3i$ is also a root. The product of the roots is $\frac{13}2$ , and $(2+3i)(2-3i)=13$ , so the real root is $\frac12$ .

JEE Main 2015 · 10 Apr · Shift 1, Mathematics question 63