IM Alg2.3.19 Lesson: Real and Non-Real Solutions
What do you notice? What do you wonder?
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[/img][/td][td][math]f(x)=2x^2+4x[/math][br][math]f(x)=0[/math] when [math]x=0,\text{-}2[/math][/td][/tr][tr][td][img]data:image/png;base64,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[/img][/td][td][math]g(x)=2x^2+4x+2[/math][br][math]g(x)=0[/math] when [math]x=\text{-}1[/math][/td][/tr][tr][td][img]data:image/png;base64,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[/img][/td][td][math]h(x)=2x^2+4x+4[/math][br][math]h(x)=0[/math] when [math]x=\text{-}1+i,\text{-}1-i[/math][br][/td][/tr][/table]
Here are some equations:
Which equations will have real solutions, and which ones will not? Write your prediction in the table.[br][br]Pause here for discussion.[br]
What advice would you give to someone who is trying to figure out whether a quadratic equation has real solutions?[br]
Create three different quadratic equations. At least one should have solutions with an imaginary part, and at least one should have solutions with only real parts.
Solve your equations. Write down your equations and their solutions in the table.
IM Alg2.3.19 Practice: Real and Non-Real Solutions
Use the applet above:
[size=150]Without calculating the solutions, determine whether each equation has real solutions or not.[br][br][math]\text{-}0.5x^2+3x=0[/math][/size]
[math]x^2-4x+7=0[/math]
[math]2x^2-2x-1=0[/math]
[math]\text{-}0.5x^2+3x=3[/math]
[math]x^2-4x+7=5[/math]
[math]2x^2-2x-1=\text{-}4[/math]
The graph shows the equation y=2x²+0.5x-4
[img]data:image/png;base64,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[/img][br][br]Based on the graph, what number could you put in the box to create an equation that has no real solutions?[br][math]2x^2 + 0.5x - 4 = \boxed{\phantom{100}}[/math]
[size=150]The graph shows the equation [math]y=1.5x^2-3x+2[/math].[/size][br][img]data:image/png;base64,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[/img][br]Without calculating the solutions, determine whether [math]1.5x^2-3x+2=0[/math] has real solutions.[br]
Show how to solve [math]1.5x^2-3x+2=0[/math]
Write a quadratic equation that has two non-real solutions.
How did you decide what equation to write?
Find the solution or solutions to each equation.
[math]\text{-}2x^2+2x=2.5[/math]
[math]4.5x^2+3x+\frac{1}{2}=0[/math]
[math]\frac{1}{2}x^2+5x=\text{-}14[/math]
[math]\text{-}x^2-1.5x+5=7[/math]
[size=150]Elena and Kiran were solving the equation [math]2x^2-4x+3=0[/math] and they got different answers. Elena wrote[math]1\pm i\sqrt{0.5}[/math], and Kiran wrote [math]1\pm\frac{i\sqrt{8}}{4}[/math]. [/size][br]Are their answers equivalent? Say how you know.