How to find the discriminant of a polynomial?

The discriminant of a polynomial is defined as the square of its radical, which is the square root of the product of its distinct roots. The equation $ax^2+bx+c$ has two distinct roots, so its discriminant is $b^2-4ac$. If you know two distinct roots for a polynomial then you can find its discriminant.

How to find the discriminant of a quadratic polynomial?

The discriminant of a quadratic polynomial is a measure of how many solutions an equation has. It can have one, two, or no solutions. There are two types: local and global. The local discriminant is the square of the local determinant where the local determinant is the value obtained by multiplying the coefficients of the two terms whose coefficients are not equal to one. The global discriminant is the square of the local discriminant of the polynomial when evaluated at infinity

How to find the discriminant of $ax^+ bx + c$?

The discriminant of a polynomial of degree $n$ is the resultant of the polynomial P and its derivative P’. For your example, we have P equal to $ax^2+bx+c$ and P’ equal to $2ax+b$. So, the discriminant equals $b^2 - 4ac$.

How to calculate the discriminant of a quadratic equation?

The discriminant of a polynomial is the square of the coefficient of the term of highest degree. If there are two distinct roots to a quadratic equation, the discriminant must be 0. If there are no solutions, the discriminant must be equal to 0 or negative. If the discriminant is 0, the equation has no solutions. If the discriminant is negative, the solutions are imaginary.

How to find

In order to find the discriminant, we need to find roots of the polynomial. If there is no root, then the polynomial has no discriminant. If there are multiple roots, then we can use the discriminant of the derivative of the polynomial to find the discriminant. If there is no root, then the discriminant is 0.