DERIVATION OF A FORMULA

Asked by  | 10th Apr, 2008, 04:32: PM

Expert Answer:

if α ,β , γ  are the 3 zeros of a cubic polynomial  ax³ +bx² + cx +d and a not equal to 0.

then,   α+β +γ = - b/a  ,  (coefficient of  x² / coefficient of x³)  ,   α β + β γ + γ α= -c/a  (coefficient of x / coefficient of x³)  ,    and    αβγ  = - d/a  ( constant term / coefficient of x³)

Example:  3 , -1 , -1/3 are the zeros of   3x³ -5x² - 11x - 3   so we take  α = 3  ,  β  =- 1  and  γ  = - 1/3

α  + β  +γ  = 3 + (-1) + (- 1/3) = - (-5)/ 3 = -b/ a

αβ + βγ + γα  = 3x ( -1) + (-1) x (-1/3) + n(-1/3) x 3  = -11/3 = c/a.

αβγ   =3 x(-1) x(-1/3) =1 = -(-3)/3 =  -d /a

Answered by  | 17th Apr, 2008, 11:45: PM

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