Question

If (x + 1) and (x-2) are factors of the polynomial x³+ mx²+2x +n, find the values of m and n.​

Answer 1

Answer:

f(x)=x³+ mx²+2x +n

since,

(x + 1) and (x-2) are factors of the polynomial x³+ mx²+2x +n,then f(-1)=0 and f(2)=0.

[ since ,(x + 1)=0,or,x=(-1) and (x-2)=0,or,x=2]

now,

f(-1)=(-1)³+ m(-1)²+2(-1) +n=0

or,m+n=3______________________(1)

again,

f(2)=0

or,2³+ m2²+2*2+n=0

or,4m+n=(-12)______________________(2)

from (1) and (2) we get,

(1)-(2)

m+n-(4m+n)=3+12

or,-3m=15

or,m=(-5)

putting the value of m in (1) we get,

-5+n=3

or,n=8

so,m=(-5) and n=8.

this is the required answer.

Answer 2

Answer:

I HOPE THIS WILL HELP YOU

Step-by-step explanation: