Module 22.3

Using The Quadratic FormulaTo Solve Equations

What is the quadratic formula,and how can you use it to solve quadratic equations?

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Discriminant

A quadratic equation 𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0 can have two, one, or no real solutions.

By evaluating the discriminant, you can determine the number of real solutions.

If the discriminant is positive – it has two solutions.If it’s zero – it has one solution.If it’s negative – it has no solutions.

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Why does the value of the discriminant indicate the number of solutions?

When the number inside the radical sign is positive, there are two solutions, because you can take the positive and negative square root of a positive number.When the number inside the radical sign is zero, there is one solution, because the square root of 0 is 0, and adding and subtracting 0 will not change the value of –b.When the number is negative, there are no real solutions because you can’t take the square root of a negative number.

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