# Lesson 19

Real and Non-Real Solutions

### Problem 1

Without calculating the solutions, determine whether each equation has real solutions or not.

1. $$\text-0.5x^2+3x=0$$
2. $$x^2-4x+7=0$$
3. $$2x^2-2x-1=0$$
4. $$\text-0.5x^2+3x=3$$
5. $$x^2-4x+7=5$$
6. $$2x^2-2x-1=\text-4$$

$$y = \text-0.5x^2+3x$$

$$y = x^2-4x+7$$

$$y = 2x^2-2x-1$$

### Problem 2

The graph shows the equation $$y=2x^2+0.5x-4$$.

Based on the graph, what number could you put in the box to create an equation that has no real solutions?
$$\displaystyle 2x^2+0.5x-4 = \boxed{\phantom{30}}$$

### Problem 3

The graph shows the equation $$y = 1.5x^2-3x+2$$.

1. Without calculating the solutions, determine whether $$1.5x^2-3x+2=0$$ has real solutions.
2. Show how to solve $$1.5x^2-3x+2=0$$.

### Problem 4

Write a quadratic equation that has two non-real solutions. How did you decide what equation to write?

### Problem 5

Find the solution or solutions to each equation.

1. $$\text-2x^2+2x=2.5$$
2. $$4.5x^2+3x+\frac12=0$$
3. $$\frac12 x^2+5x=\text-14$$
4. $$\text- x^2 -1.5x + 5 = 7$$

### Solution

Elena and Kiran were solving the equation $$2x^2-4x+3=0$$ and they got different answers. Elena wrote $$1 \pm i\sqrt{0.5}$$, and Kiran wrote $$1 \pm \frac{i\sqrt8}{4}$$. Are their answers equivalent? Say how you know.