Question

If the zeroes of the polynomial x^3 - 3x^2 + x + 1 are a - b, a, a +b, find a and b.

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Answer 1

Step-by-step explanation:

hope you can understand....

Answer 2

Answer:

Answer:

a = 1

b = ±√2

Step-by-step explanation:

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On comparing the two equations, we get

a=1

b=−3

c=1

d=1

Given zeroes are:

α=a−b

β=a

γ=a+b

We know that in a cubic polynomial,

sum of zeroes = −

a

b

⟹α+β+γ=−

1

(−3)

⟹a−b+a+a+b=3

⟹3a=3

⟹a=3÷3=1

⟹

a=1

We also know that in a cubic polynomial,

Product of zeroes = −

a

c

⟹α×β×γ=−

a

c

⟹(a−b)(a)(a+b)=−

1

1

Put a = 1

(1−b)(1)(1+b)=−1

⟹1

2

−b

2

=−1

⟹1−b

2

=−1

⟹b

2

=1+1

⟹b

2

=2

b=±

2