Question

Find the value of a and b if

x- 1

and

x -2

are factors of

x3-ax+b.

Answer 1

if x-1 and x-2 are factors of x^3-ax+b
then x-1=0 and x-2=0
x=1 and x=2
now putting x=1 and x=2 in the eqn and solving simultaneously we get
1-a+b=0 -------(1)
8-2a+b=0-----(2)
we can write the eqns as
-a+b = -1
-2a+b = -8
changing the sign of eqn (2) we get
-a+b = -1
2a-b = 8
---------------
a = 7
now putting the value of a in eqn (1) we get
-7+b = -1
b = -1+7
b = 6