An equation of the form ax^2 + bx + c = 0, where a, b, c are real numbers but a ≠ 0. is called a quadratic equation.
A quadratic equation in which terms are arranged in descending order of their degrees is called the standard form of the equation. That is, ax^2 + bx + c = 0, a ≠ 0
The roots of the quadratic equation: a real number α is called a root of the quadratic equation if a α2 + bα + c = 0
Method of completing the square:
If b^2 – 4ac < 0, then there is no real number This is because square is b^2 – 4ac. Therefore, there are no real roots for the given quadratic equation in this case.
Since b^2 – 4ac determines whether the quadratic equation ax^2 + bx + c = 0 has real roots or not, D = b^2 – 4ac is called the discriminant of this quadratic equation