Integer coefficients don't make any difference. If the coefficients are real, then for odd degree, there has to be (as trambolin notes) at least one real root. For quadratic, the discriminant has to be non-negative. For higher even degree it is more complicated. Try looking at Sturm sequences.Dragonfall said:I'll try my luck here:
How do you determine whether an integer coefficient single variable polynomial has at least one real root?
An integer polynomial is a mathematical expression consisting of constants, variables, and operations of addition, subtraction, and multiplication, where all the coefficients and exponents are integers.
The degree of an integer polynomial is the highest exponent of its variable term. For example, in the polynomial 3x^2 + 5x + 1, the degree is 2.
No, an integer polynomial cannot have negative exponents. This is because all the coefficients and exponents in an integer polynomial must be integers, and negative exponents result in fractions or decimals.
An integer polynomial is a type of polynomial where all the coefficients and exponents are integers, while a regular polynomial can have coefficients and exponents that are any real numbers.
Integer polynomials are commonly used in fields such as physics, engineering, and computer science to model and solve problems involving whole numbers. They are also used in cryptography to encrypt and decrypt data.