Polynomial Equations
http://www.maa.org/taxonomy/term/41368/0
enRaising the Roots
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/raising-the-roots
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The article describes how to find polynomials whose roots are given powers of the roots of an original polynomial.</em></p>
</div></div></div>A Simple Solution of the Cubic
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-simple-solution-of-the-cubic
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><I>A simple symmetric way of solving the cubic equation.</I></div></div></div>Finding Rational Roots of Polynomials
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/finding-rational-roots-of-polynomials
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><i>Two little known results when integral polynomials have rational roots</i></p>
</div></div></div>Nice Cubic Polynomials for Curve Sketching
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/nice-cubic-polynomials-for-curve-sketching
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>Using Pythagorean triplets to construct cubic polynomials such that the polynomial and its first and second derivatives have integer roots.</em></p>
</div></div></div>Nice Cubic Polynomials, Pythagorean Triples, and the Law of Cosines
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/nice-cubic-polynomials-pythagorean-triples-and-the-law-of-cosines
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The authors discuss a systematic way of constructing cubic polynomials with rational roots and critical points.</em></p>
</div></div></div>Proof without Words: The Arithmetic-Geometric Mean Inequality for Three Positive Numbers
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/proof-without-words-the-arithmetic-geometric-mean-inequality-for-three-positive-numbers
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>A visual proof is given for the arithmetic mean -- geometric mean inequality for three numbers.</em></p>
</div></div></div>A Matrix Proof of Newton's Identities
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-matrix-proof-of-newtons-identities
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>Newton’s identities relate the coefficients of a polynomial to sums of powers of its roots. The author uses the Cayley-Hamilton theorem and properties of the trace of a matrix to derive Newton’s identities.</em></p>
</div></div></div>Quadratic Equations: From Factored to Standard Form
http://www.maa.org/programs/faculty-and-departments/course-communities/quadratic-equations-from-factored-to-standard-form
Lesson 35: Polynomial Functions
http://www.maa.org/programs/faculty-and-departments/course-communities/lesson-35-polynomial-functions