Question

Can anyone kindly help me with a math question about polynomial attached below?

Answer 1

Answer:

f(ρ) = aρ + b      ... (1)

f(γ) = aγ + b      ... (2)

Subtracting (2) from (1) gives:

f(ρ) - f(γ) = a ( ρ - γ )   =>   a = ( f(ρ) - f(γ) ) / ( ρ - γ )

Subtracting γ times (1) from ρ times (2) gives:

ρf(γ) - γf(ρ) = b ( ρ - γ )   =>   b = ( ρf(γ) - γf(ρ) ) / ( ρ - γ )

Thus

f(x) = ax + b

    = (  ( f(ρ) - f(γ) ) x  +  ρf(γ) - γf(ρ)  ) / ( ρ - γ )

    = (  ( f(ρ) ( x - γ )  -  f(γ) ( x - ρ )  ) / ( ρ - γ )