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+1 vote
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in Polynomials by (44.3k points)

If the zeros of the polynomial f(x) = x3 – 3x2 + x + 1 are (a – b), a and (a + b), find a and b.

1 Answer

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Best answer

Given: Zeros of the polynomial x3 – 3x2 + x + 1 are (a – b), a and (a + b).

Now by using the relationship between the zeros of the quadratic polynomial we have:

Sum of zeros = -(coefficient of x)/(coefficient of x2) = -1

a – b + a + a + b = -1

3a = 3

a = 1

Product of zeros = (constant term)/(coefficient of x2) = -1

(a – b) (a) (a + b) = -1

(1 – b) (1) (1 + b) = – 1

1 – b2 = – 1

b = ±√2

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