Question
Find a polynomial of degree 4 that has a integer coefficients and zeros 1,-1,2 and 1/2 (one half)?
Answers
Bosnian
x ^ 4 + a x ^ 3 + b x ^ 2 + c x + d =
( x - x1 ) ( x - x2 ) ( x - x3 ) ( x - x4 ) =
( x - 1 ) [ x - ( - 1 ) ] [ x - 2 ) ] ( x - 1 / 2 )
( x - 1 ) ( x + 1 ) ( x - 2 ) ( x - 1 / 2 ) =
x ^ 4 - 5 x ^ 3 / 2 + 5 x / 2 - 1
( x - x1 ) ( x - x2 ) ( x - x3 ) ( x - x4 ) =
( x - 1 ) [ x - ( - 1 ) ] [ x - 2 ) ] ( x - 1 / 2 )
( x - 1 ) ( x + 1 ) ( x - 2 ) ( x - 1 / 2 ) =
x ^ 4 - 5 x ^ 3 / 2 + 5 x / 2 - 1