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Using the Quadratic Formula to find Complex Roots

Using the Quadratic Formula to find Complex Roots 1.11 - Solution

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We want to use the discriminant of the given quadratic equation to determine the number and type of solutions. In the Quadratic Formula, is the discriminant. If we just want to know the number and type of solutions, and not the solutions themselves, we only need to work with the discriminant. Let's first write all the terms on the left-hand side. Having rewritten the equation, we can now identify the values of and Finally, let's evaluate the discriminant.
Simplify
Since the discriminant is greater than zero, the quadratic equation has two real solutions.

Extra

Further information
If the discriminant is greater than zero, the equation will have two real solutions. If it is equal to zero, the equation will have one real solution. Finally, if the discriminant is less than zero, the equation will have no real solutions.

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