Ads
related to: real and equal roots condition chart for word problems worksheetteacherspayteachers.com has been visited by 100K+ users in the past month
- Worksheets
All the printables you need for
math, ELA, science, and much more.
- Lessons
Powerpoints, pdfs, and more to
support your classroom instruction.
- Free Resources
Download printables for any topic
at no cost to you. See what's free!
- Projects
Get instructions for fun, hands-on
activities that apply PK-12 topics.
- Worksheets
Search results
Results from the WOW.Com Content Network
Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
The rule states that if the nonzero terms of a single-variable polynomial with real coefficients are ordered by descending variable exponent, then the number of positive roots of the polynomial is either equal to the number of sign changes between consecutive (nonzero) coefficients, or is less than it by an even number.
If >, the cubic has three distinct real roots; If <, the cubic has one real root and two non-real complex conjugate roots. This can be proved as follows. First, if r is a root of a polynomial with real coefficients, then its complex conjugate is also a root. So the non-real roots, if any, occur as pairs of complex conjugate roots.
whose solutions are called roots of the function. The derivative of a cubic function is a quadratic function. A cubic function with real coefficients has either one or three real roots (which may not be distinct); [1] all odd-degree polynomials with real coefficients have at least one real root.
When there is only one distinct root, it can be interpreted as two roots with the same value, called a double root. When there are no real roots, the coefficients can be considered as complex numbers with zero imaginary part, and the quadratic equation still has two complex-valued roots, complex conjugates of each-other with a non-zero ...
It follows from the present theorem and the fundamental theorem of algebra that if the degree of a real polynomial is odd, it must have at least one real root. [2] This can be proved as follows. Since non-real complex roots come in conjugate pairs, there are an even number of them;
For polynomials with real coefficients, it is often useful to bound only the real roots. It suffices to bound the positive roots, as the negative roots of p(x) are the positive roots of p(–x). Clearly, every bound of all roots applies also for real roots. But in some contexts, tighter bounds of real roots are useful.
The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
Ads
related to: real and equal roots condition chart for word problems worksheetteacherspayteachers.com has been visited by 100K+ users in the past month