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Show That All of The Real Zeros of P (X) x4 - 3x2 + 2x - 5 Lie Between - 3 and 2

The document contains 3 problems involving finding real zeros or roots of polynomials: 1) Show that all real zeros of x^4 - 3x^2 + 2x - 5 lie between -3 and 2. 2) Find upper and lower bounds for 2x^3 + x^2 - 9x + 2. 3) Find all real solutions to 3x^4 + 4x^3 - 7x^2 - 2x - 3 = 0 by listing rational roots, using Descartes' Law of Signs to predict positive and negative roots, and showing there are no rational roots while locating upper and lower bounds.

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Axel Gayondato
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111 views1 page

Show That All of The Real Zeros of P (X) x4 - 3x2 + 2x - 5 Lie Between - 3 and 2

The document contains 3 problems involving finding real zeros or roots of polynomials: 1) Show that all real zeros of x^4 - 3x^2 + 2x - 5 lie between -3 and 2. 2) Find upper and lower bounds for 2x^3 + x^2 - 9x + 2. 3) Find all real solutions to 3x^4 + 4x^3 - 7x^2 - 2x - 3 = 0 by listing rational roots, using Descartes' Law of Signs to predict positive and negative roots, and showing there are no rational roots while locating upper and lower bounds.

Uploaded by

Axel Gayondato
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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Show that all of the real zeros of P(x)= x4 - 3x2 + 2x - 5 lie between -3 and 2.

Find the upper and lower bounds for P(x) = 2x3 + x2 - 9x +2

Find all real solutions:


P(x) = 3x4 + 4x3 - 7x2 - 2x - 3 = 0
a) List the possible rational roots.
b) Use Descartes' Law of Signs to predict the possible number of positive
and negative real roots.
c) Show that P(x) does not have any rational roots, and also locate the upper and lower bounds.

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