EMILE : Enseignement d'une Matière Intégrée à une Langue Étrangère

The quadratic formula can be used to solve any quadratic equation. Quadratic equations take the form ax²+bx+c=0 , where abc and are numbers and x is the unknown.

A quadratic equation includes:

  • a non-zero real number multiplied by  ,

  • a number multiplied by x

  • and a number by itself.

 Quadra01 

The quadratic formula allows any quadratic equation to be solved. Substitute the different values in the equation into the quadratic formula to solve the equation.

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To use the quadratic formula, substitute the values for ab, and c, and in a given equation into the formula, then work through the formula to find the answers. Take great care with the sign (+,-) of ab, and c.

 
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Given a quadratic equation, work out the values of ab, and c. Once these values are known, substitute them into the quadratic formula, making sure that their positive and negative signs do not change.

In this example, a is 1, b is 3, and c is -2.

Quadra04

The number of solutions of a quadratic equation depends on the result of that is called discriminant and denoted .

Δ = b² - 4ac

  • If is negative, then no possibility of calculate the square root.

Therefore, no real solution.

  • If is null, then only 1 solution because √0=0 and:

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  • if is positive, then 2 solutions:

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