- Roots of Algebraic and Transcendental Equations

Case 1: If <+( ) ( ) 012f x f xi i , then the root lies between xi and + 12xi .

Case 2: If >+( ) ( ) 012f x f xi i , then the root lies between + 12xi and +1xi .

Case 3: If =+( ) ( ) 012f x f xi i , then xi or + 12xi is a real root.