Question

if the zeroes of the polynomial x3 -3x2+x+1 are a-b, a,a+b, find a and b

Answer 1

given, p (x)= x3-3x2+x+1

and it's zeroes are a-b, a, a+b

on comparing with ax3+bx2+cx+d

we get, a= 1, b= -3, c= 1, d = 1

now,

sum of the zeroes = -b/a

a-b+a+a+b = -(-3/1)

3a = 3

a= 3/3=1 ----------(1)

product of the zeroes=-d/a

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

a (a2-b2) = -1

1 ( 12- b2)= -1

1- b2= -1

-b2= -1-1

-b2= -2

b2= 2

b= plus minus root 2

Answer 2

Answer:

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