Question

Find the value of a and b if

x -1

and

x -2

are factors of

3

x- ax -b .

Answer 1

x4 + ax3 - 3x2 + 2x + b

If we know our two factors, then we know our zeros. Our zeros are -1 and 1. What we can do is plug in x=-1 into the polynomial and set it equal to zero. Then we do the same for x=1.

1 - a - 3 - 2 + b = 0 ---> for x=-1
-a + b = 4


1 + a - 3 + 2 + b = 0 ---> for x=1

a + b = 0


Now we have a system of equations to work with.

-a + b = 4 eq1
a + b = 0 eq2


Add the two equations to eliminate the a terms.

2b = 4

b = 2


Substitute this value of b into any of the equations to solve for a.

a = -2

Answer 2

equations
3x-ax-b=0

3-a-b=0
a+b=3
6-2a-b=0
2a+b=6
a+a+b=6
a+3=6
a=3
b=0