Question

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

Answer 1

let f(x) = x3+10x2+ax+b
when x-1=0, x=1
therefore remaninder1 = 0
--> f(1) = 0
--> 1 + 10 +a + b=0
--> a+b=-11 -------(1)

when x+2=0, x=-2
Remainder(2) = 0
--> f(-2)=0
--> - 8 + 40 - 2a +b=0
--> 2a-b=32 ----(2)

Equating (1) and (2)
a + b = -11
2a - b = 32
____________
3a =  21
--> a=7

Substiture a = 7 in (1)
Therefore 7 + b = -11
--> b = -11-7
--> b = -18

Therefore a=7 and b=-18
Hope my answer was helpful :) :)