Question

4. Determine the values of a and b in the
following if:
(i) (x - 1) and (x - 2) are factors of
x² – ax+b.​

Answer 1

Answer:

1) It is given that x-1 and x-2 are factors of x3-ax+b, so the value of the x will be 1 and 2.

2)  Put the value of x in the given equation one by one we get the equation in terms of a and b. While putting the values in the equation it gives us answer as 0 because they are the factor of the given equation.

Putting x = 1

x³-ax+b

1³-a.1+b=0

a-b = 1------------------------(I)

Putting x = 2

x³-ax+b

2³-a.2+b=0

8-2a+b=0

2a-b=8--------------(II)

3) Subtract the equation (I) from (II)

   2a-b=8

-    a-b = 1

      a  =  7

On solving we get the value of b as 6

The values of a and b are 7 and 6 respectively.