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**5.6 Quadratic Equations and Complex Numbers**

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The Discriminant When using the Quadratic Formula you will find that the value of b2 - 4ac is either positive, negative, or 0. b2 - 4ac called the Discriminant of the quadratic equation.

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**What the Discriminant Tells Us…**

If it is positive then the formula will give 2 different answers If it is equal to zero the formula will give only 1 answer This answer is called a double root If it is negative then the radical will be undefined for real numbers thus there will be no real zeros.

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**Finding the Discriminant**

Find the Discriminant and determine the numbers of real solutions. Example 1: x2 + 5x + 8 = 0 How many real solutions does this quadratic have? b/c discriminant is negative there are no real solutions

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**Finding the Discriminant**

Find the Discriminant and determine the numbers of real solutions. Example 2: x2 – 7x = -10 How many real solutions does this quadratic have? b/c discriminant is positive there are 2 real solutions

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**Imaginary Numbers What if the discriminant is negative?**

When we put it into the Quadratic Formula can we take the square root of a negative number? We call these imaginary numbers An imaginary number is any number that be re written as:

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Imaginary Numbers Example 1: Example 2:

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Complex Numbers A complex number is any number that can be written as a + bi, where a and b are real numbers; a is called the real part and b is called the imaginary part.

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**Operations with Complex Numbers**

Find each sum or difference: (-3 + 5i) + (7 – 6i) = (-3 – 8i) – (-2 – 9i) =

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**Operations with Complex Numbers**

Multiply: (2 + i)(-5 – 3i) =

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**Operations with Complex Numbers**

Multiply: (3 - i)(4 – 7i) =

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