Polynomials

  Let α = a - d  ,  β = a , γ =a +d be the zeros of the polynomial f ( x ) = 2x³ - 15 x² + 37x - 30

  α + β + γ = - ( -15 ) / 2 = 15/2.

  αβγ  =- ( -30 )/  2 = 15

 ( a - d ) + a + ( a + d ) = 15/2

 ( a - d ) a ( a + d ) = 15

 3a = 15/2  and   a (   a² - d² ) = 15

 a = 15/ 6 = 5 /2.    and  5/2 ( 25 / 4 - d² ) = 15

a = 5/ 2  ,    and   d = ±1 / 2

 α = a - d = 5/2 - 1/2 = 2 ,  β 5/2  ,  γ =a + d = 5 /2 + 1 / 2 = 3

  Hence the zeros of the given polynomial are  2 , 5/2 , 3