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The teachers  ### ax² + bx +c = 0 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.  ### b² − 4ac = 0

In this case, the quadratic equation has a double solution.  ### b² − 4ac < 0

In this case, the quadratic equation has no real solutions.  ## Properties of the Solutions to Quadratic Equations

The sum of the solutions of a quadratic equation is: The product of the solutions of a quadratic equation is: If the roots of an equation are known, it can be writen as: 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

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