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.
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Information: IM Alg2.3.19 Practice: Real and Non-Real Solutions