Question

find the value of a and b such that (x +1 ) and (x +2 ) are the factors of polynomial x² + ax - bx + 10​

Answer 1

Answer:

p(x)=x3 +ax2-bx+10

g(x)=x+1

put g(x)=0

x+1=0

x=-1

g(x) is a factor of p(x)

therefore ,p(-1)=0

(-1)3 + a(-1)2 -b(-1)+10

-1+a+b+10=0

a+b+9=0

a=-9-b...(1)

f(x)=x+2

put f(x)=0

x+2=0

x=-2

f(x) is a factor of p(x)

therefore p(-2)=0

(-2)3+a(-2)2-b(-2)+10=0

-8+4a+2b+10=0

4a+2b+2=0

putting the value of a from equation...(1)

4(-9-b)+2b+2=0

-36-4b+2b+2=0

-34-2b=0

-2b=34

b=-34/2

b=-17

put the value of b in equation (1)

A=-9-(-17)

A=-9+17

A=8

hope it helps you