Question

find the value of a and b so that the polynomial x³+10x²+ax+b is exactly divisible by (x-1)as well as by (x+2)​

Answer 1

Step-by-step explanation:

By factor theorem,

(x-1)=0

x=1

P(1)=1^3+10*1^2+a*1+b=0

=1+10+a+b=0

=11 a+b=0

=a+b= -11......(i)

By factor theorem

(x +2)=0

x =-2

P(-2)=-2^3+10*-2^2+a*-2+b=0

= - 8-40-2a+b=0

=-48-2a+b=0

=-2a+b=48

=a+b=48/2

=a+b=24......(ii)

From i & ii we get

a+b+a+b=24+(-11)