Question

Find the values of a and b if (x-1) and (x-2) are factors of x2 -ax+b.

Answer 1

Given -

(x-1) and (x-2) are factors of x²-ax+b

To find-

The values of a and b

Solution -

(x-1) is a factor of x²-ax+b

Therefore,

x-1=0

x=1

Now,

p(x)=x²-ax+b

Putting the value of x=1 we will get

p(1)=(1)²-a×1+b

p(1)=1-a+b

(x-1) is a factor of x²-ax+b

1-a+b=0

b=a-1..........1)

Now,

(x-2) is a factor of x²-ax+b

Therefore,

(x-2)=0

x=2

Now,

p(x)=x²-ax+b

Putting the value of x =2 we will get

p(2)=(2)²-a×2+b

p(2)=4-2a+b

(x-2) is a factor of x²-ax+b

4-2a+b=0

4-2a+a-1=0[By 1]

-a+3=0

a=3

Now putting the value of a=3 in equation 1) we will get

b=3-1

b=2

Therefore the value of a is 3 and b is 2