Polynomials
Asked by
| 26th Apr, 2008,
09:42: PM
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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