Quadratic Equations: Real and Complex Roots, Discriminant A quadratic equation in the form of $$ax^2 + bx + c = 0$$ is a mathematical equation where a, b, a...
Quadratic Equations: Real and Complex Roots, Discriminant
A quadratic equation in the form of is a mathematical equation where a, b, and c are real numbers. A quadratic equation can have either two real roots (if a and b are both positive or both negative) or one real root (if a and b are both negative).
The roots of a quadratic equation are the values of x that make the equation equal to zero. The roots can be found by using the quadratic formula:
The discriminant of a quadratic equation is a value that can be calculated from the coefficients of the quadratic equation. The discriminant is given by the expression and is a measure of the nature of the roots of the quadratic equation.
If the discriminant is positive, the quadratic equation has two real roots.
If the discriminant is negative, the quadratic equation has only one real root.
If the discriminant is zero, the quadratic equation has two complex roots