Q. If $f(x) = 2x^{3} + mx^{2} - 13x + n$ and 2, 3 are roots of the equation $f(x) = 0$, then the values of $m$ and $n$ are
A) -5, -30
B) -5, 30
C) 5, 30
D) None of these
Explanation
(b)
Since, 2 and 3 are the roots of the equation $2x^{3} + mx^{2} - 13x + n = 0$
$\therefore\ \ f(2) = 2(2)^{3} + m(2)^{2} - 13(2) + n = 0$
And $f(3) = 2(3)^{3} + m(3)^{2} - 13(3) + n = 0$
$\Rightarrow 4m + n = 10$ and $9m + n = - 15$
$\Rightarrow m = - 5,\ \ \ \ n = 30$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.