Question

12.Find the values of a and b so that the polynomial x3 +10x2+ax+b is exactly divisible by x-1 as well as x-2.

Answer 1

x-1=0 (use remainder theorem)
That implies x=1.
Substitute x=1 in the equation.
That implies 1^3+10(1)^2+a(1) + b=0 (Remainder theorem)
1+10+a+b=0
a+b= -11
a= -11-b .......(1)

Now,
x-2=0
x=2
Substitute in the equation.
2^3+10(2)^2 + a(2) + b=0
Substitute value of 'a' from (1).
8+40+2(-11-b) + b=0
48-22-22b=0
26=22b
b=26/22=13/11
a= -11-13/11
a= -144/11