Tool to compute the discriminant of a polynomial. A discriminant of a polynomial is an expression giving information about the nature of the roots of the polynomial.

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Tool to compute the discriminant of a polynomial. A discriminant of a polynomial is an expression giving information about the nature of the roots of the polynomial.

Answers to Questions

How to calculate a discriminant?

For a quadratic polynomial, the discriminant named delta is calculated like this:

$$ \Delta = b^2-4ac $$

The fact of knowing the value of the discriminant then solves the equation.

If the discriminant is positive (strictly), the equation has two solutions:

$$ x_1 = \frac {-b + \sqrt \Delta}{2a} $$

$$ x_2 = \frac {-b - \sqrt \Delta}{2a} $$

If the discriminant is zero, the equation has a double root:

$$ x_1=x_2 = -\frac b{2a} $$

If the discriminant is negative (strictly), the equation has complex solutions:

$$ \delta^2 = \Delta $$

$$ x_1 = \frac {-b + \delta}{2a} $$

$$ x_2 = \frac {-b - \delta}{2a} $$

For equations of higher degrees, the calculations are much more complicated, but knowledge of the determinants is important.

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