quadratics and imaginary numbers review eq: how do i solve ... · 1/10/2015 · notes quadratic...
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Quadratics and Imaginary Numbers Review
EQ: How do I solve a quadratic?
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Operating with Imaginary Numbers
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Simplifying Imaginary Numbers
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Operating with Imaginary Numbers
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Complex Numbers
Always take the form (a + bi)
The real portion comes first, the imaginary second
Complex Conjugate: (a bi)
(2x 3i)(2x + 3i)
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Multiplying and Dividing Complex Numbers
5i(6 3i)
(2 + 4i)(6 9i)
(3 i)(2 + i)
(6 7i)(6 + 7i)
(3 2i)(4 + i)
(6 + 4i)(1 3i)
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Standard form of a Quadratic
ax2 + bx + c = 0
Discriminant: b2 4ac
Discriminant > 0: 2 real rootsDiscriminant = 0: 1 real root
Discriminant < 0: 2 imaginary roots
![Page 8: Quadratics and Imaginary Numbers Review EQ: How do I solve ... · 1/10/2015 · Notes Quadratic and Imaginary Numbers Review.notebook 5 January 20, 2015 Jan 199:39 PM Complex Numbers](https://reader033.vdocument.in/reader033/viewer/2022060600/60548acb4c90bd7b4a3fdca7/html5/thumbnails/8.jpg)
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Solving a Quadratic
Solve by 1 of 3 ways:a. Factoringb. Completing the Squarec. Quadratic Formula
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Solving a Quadratic by Factoring
1. Set equal to 0.
2. Factor.
3. Set each factor equal to 0 and solve for the variable.
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Examples of Solving by Factoring1. 6x2 = 2x 3. 2x2 + 2x + 15 = 15x
2. 2x2 6x = x2 + 27 4. 5x3 + 6x2 = 9x2 10x
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Solving a Quadratic by Completing the Square
1. Set equal to 0.
2. Factor out a from ax2 + bx to make
3. Move constant to the other side of the equation.
4. Add to each side of the equation to make a perfect square.
5. Factor the perfect square.
6. Squareroot each side and set factor equal to the positive and negative root.
7. Solve for the variable.
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Examples of Solving by Completing the Square
1. x2 8x 12 = 0
2. 2x2 8x + 8 = 4
3. 6x2 + 3 = 11x
4. 3x2 3x = 8
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Solving by Quadratic Formula
1. Set equal to zero.
2. Label a, b, and c by ax2 + bx + c = 0.
3. Plug into the formula and simplify.
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Examples of Solving by Quadratic Formula1. 6x2 = 2x
2. x2 8x = 16
3. 4x2 + 6x = 30
4. 2x2 + 2x + 15 = 15x
5. 6x2 = 9x2 10