Solutions to Quadratic Equations

ax2 + bx +c = 0

Quadratic Formula

b2 − 4ac is called the discriminant of the quadratic equation and determines the number of solutions in each equation. Three cases can be distinguished:

b2 − 4ac > 0

In this case, the quadratic equation has two solutions, which are distinct real numbers.

Quadratic Equation

Quadratic Operations

b2 − 4ac = 0

In this case, the quadratic equation has a double solution.

Quadratic Equation

Quadratic Operations

b2 − 4ac < 0

In this case, the quadratic equation has no real solutions.

Quadratic Equation

Quadratic Operations


Properties of the Solutions to Quadratic Equations

The sum of the solutions of a quadratic equation is:

Quadratic Expression

The product of the solutions of a quadratic equation is:

Quadratic Expression

Quadratic Equation from Solutions

If the roots of an equation are known, it can be writen as:

Quadratic Expression

Where:

S = x1 + x2

P = x1 · x2


Write a quadratic equation whose solutions are: 3 and 2.

S = 3 − 2 = 1

P = 3 · (−2) = −6

x2 − x − 6 = 0