Question

33. If both (x + 1) and (x - 1) are factors of ax + x square
- 2x + b, find the values of 'a' and 'b'.​

Answer 1

Answer:

a=2 and b= -1.

Step-by-step explanation:

We have : ax+x2-2x+b

The factors are (x+1)  and (x-1) .

So, x=-1 and x=1.

Put x=1 in eqation , we get

= a(1)+(1)2-2(1)+b=0

= a+1-2+b=0

= a+b-1=0

=a+b=1                                            …(1)

Put x=-1 in eqation , we get

= a(-1)+(-1)2-2(-1)+b=0

=  -a+1+2+b=0

=  -a+3+b=0

=  -(a-3-b)=0

= a-3-b=0

= a-b= 3                                             …(2)

Sub. (1) from (2) , we get

a-b-(a+b)=3-(1)

a-b-a-b=3-1

-2b=2

B=-1

Put value of b in (2), we get

a-(-1)=3

a=3-1

a=2

Hence, a=2 and b= -1.