Polynomials

Asked by  | 26th Apr, 2008, 09:42: PM

Expert Answer:

  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

 

Answered by  | 27th Apr, 2008, 08:48: PM

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