Question

if ( x + 2) and ( x - 1) are factors of ( x^3 +10x^2 + m x + n) then find the value of m & n?


plz do it fast.....

Answer 1

As x+2 is factor: let x+2=0 hence x=-2
Now f(x)=x^3+10x^2+Mx+n
F(-2)=-2^3+10*-2^2+m*-2+n
As f(x) is factor given in question therefore f(-2)=0
0=-8+40-2m+n
2m-n=32.....(1)
Now given x-1/is factor therefore let x-1=0 hence x=1
Now f(x)= x^3+10x^2+MX+n
F(1)=1^3+10*1^2+m*1+n
As f(1) is factor therefore f(x)=0
Now 0=1+10+m+n
-m-n=11...(2)
Now from 1 and 2
Solve simultaneously
: -1(2m-n=32)
-1(-m-n=11)
-2m+n=-32
1m+n=-11
- - +
-3m=-21
Therefore m=7 answer
And substitute value of m in 1
Hence 2m-n=32
2(7)-n=32
14-32=n
N=-18 answer