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Polynomial Resultants

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Questions and Answers

Which mathematical concept is the resultant closely related to?

Eliminant

Discriminant (correct)

Coefficients

Roots

What is the purpose of computing the resultant of two polynomials?

To find their sum

To find their common factor (correct)

To find their common root

To find their product

What is the resultant widely used for in number theory?

Cylindrical algebraic decomposition

Integration of rational functions

Drawing of curves defined by a bivariate polynomial equation

All of the above (correct)

What is another name for the resultant in some older texts?

Eliminant Signup and view all the answers

Can the resultant of two polynomials with rational or polynomial coefficients be computed efficiently on a computer?

Yes Signup and view all the answers

What is a resultant force in physics and engineering?

A force that is obtained by combining a system of forces and torques acting on a rigid body Signup and view all the answers

How is the resultant force calculated and visualized?

Through computational analysis or a free body diagram Signup and view all the answers

What determines the associated torque of the resultant force?

The point of application of the resultant force Signup and view all the answers

Why is the term 'resultant force-torque' sometimes used?

To refer to both the forces and torques acting on a rigid body Signup and view all the answers

What does the diagram illustrate?

Simple graphical methods for finding the line of application of the resultant force of simple planar systems Signup and view all the answers