Question

Find the value of a & b so that the polynomial x³+10x²+ax+b has (x-1) & (x+2) as factors.

Answer 1

substituting the value of x=1from 1st factor in the polynomial.
1*1*1+10*1*1+1*a+b=0
1+10+a+b=0
a+b= -11
now substituting value of x= -2from factor 2nd in the polynomial.
-2*2*2+10*-2*-2-2a+b=0
-8+40-2a+b=0
32-2a+b=0
2a+b=32
subtracting 2a+b=32 from a+b= -11
-a= -43
a=43
substituting a=43 in a+b= -11
43+b= -11
b= -11-43
b=-53