if the zeroes of the polynomial p ( x) are a-b ,a and a+b ,find a and b

Asked by deepita0 | 16th May, 2009, 11:49: AM

Expert Answer:

a-b, a+b and a are the roots of the polynomial

Sum of the roots of a cubic polynomial = -(coefficient of x2 )/(coefficient of  x3)

a-b + a+b+ a = 3

3a = 3

a =1

Product of the roots of a cubic polynomial = (constant term )/(coefficient of  x3) 

(a-b)(a+b)a = 1

(1-b2) = 1

b = 0

Also, (a-b)a + (a+b)a + (a-b)(a+b) =- (coefficient of x )/(coefficient of  x3) 

(a-b)a + (a+b)a + (a-b)(a+b) = -1

1-b + 1+ b + 1 - b2  = -1

- b2 = -4

b = +2, -2

 

Answered by  | 16th May, 2009, 03:35: PM

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