Whenever you need the brain capacity and elasticity that you gained by learning it. And you'll have a bit of an edge over the people who didn't. Being able to use clear abstract thinking is a transferable skill.
As with most advanced math, if your "real life" involves engineering work, you will use such math; otherwise, you will hardly have anything to do, in this case, with polynomial functions.
It depends on the domain. In the complex domain, a polynomial of order n must have n solutions, although some of these may be multiple solutions. In the real domain, a polynomial of odd order must have at least one real solution, while a polynomial of even order may have no real solutions.
You forgot to copy the polynomial. However, the Fundamental Theorem of Algebra states that every polynomial has at least one root, if complex roots are allowed. If a polynomial has only real coefficients, and it it of odd degree, it will also have at least one real solution.
A polynomial of degree ( n ) can have at most ( n ) real zeros. This is a consequence of the Fundamental Theorem of Algebra, which states that a polynomial of degree ( n ) has exactly ( n ) roots in the complex number system, counting multiplicities. Therefore, while all roots can be real, the maximum number of distinct real zeros a polynomial can possess is ( n ).
A polynomial in real life can be seen in various contexts, such as calculating the trajectory of a projectile, where the height of the projectile over time can be modeled by a quadratic polynomial. Additionally, polynomials are used in economics to model cost and revenue functions, helping businesses predict profits based on different levels of production. They also appear in computer graphics for rendering curves and surfaces, allowing for smooth transitions and shapes in visual design.
As with most advanced math, if your "real life" involves engineering work, you will use such math; otherwise, you will hardly have anything to do, in this case, with polynomial functions.
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you can use it house or at the mall or anywhere
Pharmacists and the makers of drugs use polynomial division. They use this type of division to help create formulas to make sure that the proper amount of drug is being distributed to the patients depending on the variables involved.
In a mathematics exam.
1+x2 is a polynomial and doesn't have a real root.
That depends on what you mean with "real-life". You won't need polynomial functions to sell stuff at a supermarket, or to cut off a dead branch from your tree... but if you work in science and engineering, you will need some really advanced math - much more than a simple polynomial function.
A third degree polynomial could have one or three real roots.
It depends on the domain. In the complex domain, a polynomial of order n must have n solutions, although some of these may be multiple solutions. In the real domain, a polynomial of odd order must have at least one real solution, while a polynomial of even order may have no real solutions.
Sort of... but not entirely. Assuming the polynomial's coefficients are real, the polynomial either has as many real roots as its degree, or an even number less. Thus, a polynomial of degree 4 can have 4, 2, or 0 real roots; while a polynomial of degree 5 has either 5, 3, or 1 real roots. So, polynomial of odd degree (with real coefficients) will always have at least one real root. For a polynomial of even degree, this is not guaranteed. (In case you are interested about the reason for the rule stated above: this is related to the fact that any complex roots in such a polynomial occur in conjugate pairs; for example: if 5 + 2i is a root, then 5 - 2i is also a root.)
You forgot to copy the polynomial. However, the Fundamental Theorem of Algebra states that every polynomial has at least one root, if complex roots are allowed. If a polynomial has only real coefficients, and it it of odd degree, it will also have at least one real solution.
A quadratic polynomial must have zeros, though they may be complex numbers.A quadratic polynomial with no real zeros is one whose discriminant b2-4ac is negative. Such a polynomial has no special name.