Question

If ( x+2) and (x -1) are the factors of ( x3

+ 10x2

+ mx + n), then find the values of m and n.
​

Answer 1

Answer:

m=7, n= -18

Step-by-step explanation:

x+2=0

x=-2

p (x)=x^3+10x^2+mx+n

p(-2)=-2^3+10×x^-2+m×-2+n

p (-2)=-8+40-2m+n

p (-2)=32-2m+n

n=2m-32

x-1=0

x=1

p (x)=x^3+10x^2+mx+n

p (1)=1^3+10×1^2+m×1+n

p (1)=1+10+m+n

p (1)=11+m+n

n= -m-11

now,

aad both answers

n=2m-32

n=-m-11

put the subtraction sigh on second eq.

n=2m-32

-n=+m+11

now,

n=2m-32 -n=+m+11

0=3m-21

21=3m

m=21÷3

m=7

n=-m-11

n= -7-11

n=-18