If `(x-alpha)` is the `H.C.F` of `x^2 +ax+ b` and `x^2+ bx +a`, then find the value of and `a +b+ 1`

If (x+1) is the HCF of (a x^(2) + bx + c) and (bx^(2) + ax + c) , then the value of c is

If (x+1) is the HCF of Ax^(2) + Bx + C and Bx^(2) + Ax + C where A n B, then the value of C is

If f(x)=(ax-b)/(bx-a) , then find the value of f(1/x) .

If x-1 is a common factor of x^(2)+ax+3 and x^(2)-bx+2 then find the value of b-a

If a+b+c=0 , then find the value of sqrt(x^a.x^b.x^c) .

If (x ^(2) + x - 2) is the HCF of the expressions (x - 1) (2x ^(2) + ax +2) and (x +2) (3x ^(2) + bx +1), then find the valued of a and b.

If (x-1)^(2) is a factor of ax3+bx2+c, find the value of a+b+c

If (x+1) is a factor of 2x^(3)+ax^(2)+2bx+1 , then find the value of a and b given that 2a-3b=4.

If f(x)=ax^(2)+bx+c and f(x - 1) = f(x) + 2x + 1. then find the values of a and b.