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- Geometry_of_roots_of_real_polynomials abstract "Graphical methods provide a means of determining or approximating the roots of a polynomial—the values that make the polynomial equal to zero. Practical tools for performing these include graph paper, graphical calculators and computer graphics.The fundamental theorem of algebra states that a nth-degree polynomial with complex coefficients (including real coefficients) has n complex roots (not necessarily real even if the coefficients are real), although its roots may not all be different from each other. If the polynomial has real coefficients, its roots are either real, or else occur as complex conjugates. Suppose a polynomial P(x) is graphed as y = P(x). At a real root, the graph of the polynomial crosses the x-axis. Thus, the real roots of a polynomial can be demonstrated graphically.For some kinds of polynomials, all the roots, including the complex roots, can be found graphically. Polynomial equations up to the fifth degree may be solved graphically.The geometrical methods of ruler and compass may be used to solve any linear or quadratic equation. Descartes showed that the constructions of Euclid were equivalent to the algebraic solution of quadratics.Cubic equations may be solved by solid geometry. Archimedes' work On the Sphere and the Cylinder provided solutions of some cubics and Omar Khayyam systematised this to provide geometrical solutions of all quadratics and cubics.".
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- Geometry_of_roots_of_real_polynomials subject Category:Elementary_algebra.
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- Geometry_of_roots_of_real_polynomials comment "Graphical methods provide a means of determining or approximating the roots of a polynomial—the values that make the polynomial equal to zero.".
- Geometry_of_roots_of_real_polynomials label "Geometry of roots of real polynomials".
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- Geometry_of_roots_of_real_polynomials sameAs Q5535525.
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