Denote the roots of `f ( x ) ` as `u , v , w . ` Because the leading coefficient of `f ` is `1 , ` we can state that `f ( x ) = ( x - u ) ( x - v ) ( x - w ) . ` Because of this, `c = -uvw , ` `b = uv + vw + uw , ` `a = - ( u + v + w ) ` (Vieta's theorem).

Further, because `g ` also has the leading coefficient `1 ` and the roots `1 / u , 1 / v , 1 / w , ` it is equal to `( x - 1 / u ) ( x - 1 / v ) ( x - 1 / w ) .`

Now consider `g ( 1 ) = ( 1 - 1 / u ) ( 1 - 1 / v ) ( 1 - 1 / w ) =`

`= 1 / ( uvw ) ( ( u - 1 ) ( v - 1 ) ( w - 1 ) ) = 1 / ( uvw ) ( uvw - ( uv + vw + uw ) + ( u + v + w ) - 1 ) ,` which is equal to `-1 / c ( -c - b - a - 1 ) = 1 + ( a + b + 1 ) / c .`

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now