Can a polynomial have no solution?

In mathematics, the Abel–Ruffini theorem (also known as Abel’s impossibility theorem) states that there is no solution in radicals to general polynomial equations of degree five or higher with arbitrary coefficients. Here, general means that the coefficients of the equation are viewed and manipulated as indeterminates.

Is the degree of a polynomial the number of solutions?

The degree of a quadratic equation is 2, thus leading us towards the notion that it has 2 solutions. The degree will always tell us the maximum number of solutions a polynomial has.

Can a polynomial equation have real and non real solutions?

George C. No. A polynomial equation in one variable of degree n has exactly n Complex roots, some of which may be Real, but some may be repeated roots.

How many solutions are in the degree 2 polynomial?

Two
In the following three examples, one can see how these polynomial degrees are determined based on the terms in an equation: y = x (Degree: 1; Only one solution) y = x2 (Degree: 2; Two possible solutions) y = x3 (Degree: 3; Three possible solutions)

Can all polynomials be solved?

So, yes, it can be done.

How do you factor a large degree polynomial?

To factor a higher degree polynomial, remove factors using synthetic or long division until you have a quadratic which can be factored or there are no more factors that can be taken out.

How many solutions are in a polynomial?

A polynomial equation of degree n has at most n solutions. A polynomial equation of degree n has exactly n solutions, if you count them with multiplicity. The equation x2+1=0 has infinitely many solutions.

What is the solution of a polynomial?

A solution of a polynomial system is a tuple of values of (x1., xm) that satisfies all equations of the polynomial system. The solutions are sought in the complex numbers, or more generally in an algebraically closed field containing the coefficients.