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This is a problem from ISI MStat 2018 PSA Problem 12 based on Sequence of positive numbers

Let , be a sequence of positive numbers such that for all n, and Let be the polynomial and suppose has no real roots for every n . Let and be the roots of the polynomial What can you say about ?

- (A) and are not real
- (B) and are real.
- (C) and are real.
- (D) and are not real

Sequence

Quadratic equation

Discriminant

Answer: is (D)

ISI MStat 2018 PSA Problem 12

Introduction to Real Analysis by Bertle Sherbert

Write the discriminant. Use the properties of the sequence .

Note that as "> has no real root so discriminant is "> so "> and ">'s are positive and decreasing so "> . So , what can we say about a ?

Therefore we can say that hence discriminant of P , must be strictly negative so option D.

This is a problem from ISI MStat 2018 PSA Problem 12 based on Sequence of positive numbers

Let , be a sequence of positive numbers such that for all n, and Let be the polynomial and suppose has no real roots for every n . Let and be the roots of the polynomial What can you say about ?

- (A) and are not real
- (B) and are real.
- (C) and are real.
- (D) and are not real

Sequence

Quadratic equation

Discriminant

Answer: is (D)

ISI MStat 2018 PSA Problem 12

Introduction to Real Analysis by Bertle Sherbert

Write the discriminant. Use the properties of the sequence .

Note that as "> has no real root so discriminant is "> so "> and ">'s are positive and decreasing so "> . So , what can we say about a ?

Therefore we can say that hence discriminant of P , must be strictly negative so option D.

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