Question

If x + 2 and x-1 are the factors of $x^3+10x^2+mx+n$, then the values of m and n are respectively

• A. 5 and -3
• B. 17 and -8
• C. 7 and-18
• D. 23 and -19

Answer 1

The correct option is C 7 and-18

Here, $x+2$ is a factor of $x^3+10x^2+mx+n$
$x=-2$
$(-2{)}^3+10(-2{)}^2+m(-2)+n=0$
$-8+40=2m-n$
$2m-n=32$ .....(i)
Again, $x-1$ is a factor of $x^3+10x^2+mx+n$
$x=1$
$1+10+m+n=0$
$m+n=-11$ .....(ii)
Adding (i) and (ii). we get,
$3m=21$
$m=7$
By putting m in (i). we get,
$2\left(7\right)-n=32$
$-n=18$
$n=-18$
Option C is correct.