Solving with Square Root

Solving with Square Root

By Kimberlee Duffin

​Roots, solutions, zeros, x intercepts

​A quadratic may have one, two, or two complex solutions or x intercepts depending on where the graph is. See the examples below:

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Two Solutions​ One Solution Two Complex or Imaginare Solutions

Multiple Choice

Use the graph to find the number of solutions or x intercepts

• 2 solutions

• 1 solution

• 3 solutions

• 2 complex or imaginary solutions

Multiple Choice

Use the graph to find the number of solutions or x intercepts

• 2 solutions

• 1 solution

• 3 solutions

• 2 complex or imaginary solutions

Multiple Select

What are the two solutions to the equation below?

$$x^2=36$$  

• 6

• -18

• 18

• -6

• 6i

Multiple Select

What are the two solutions to the equation below?

$$x^2=-100$$  

• 10i

• -100

• 100

• -10i

• 10

Multiple Choice

3x² = 12

• ± 2
• 2
• ± √12
• ± 4

Multiple Choice

-5x² = -50

• ± 5
• ± 10
• ± √10
• -10

Multiple Choice

x² + 4 = 68

• ± 8
• ± √8
• 8
• ± 64

Multiple Choice

7x² + 1 = 8

• ± 1
• ± 7
• ± √7
• ± 8

Multiple Choice

(x + 1) ² = 25

• ± 5
• 4  or  -6
• -4  or  6
• ± 4

Multiple Choice

(x - 2) ² = 9

• ± 3
• 5  or  -1
• -5  or  1
• ± 9

Multiple Choice

Use the square root technique to find the TWO solutions to the equation

(2x - 1)² = 49

• 25 or -24

• -7 or 7

• -4 or 3

• -3 or 4

Multiple Choice

What are the values of x for the equation shown?

$$\left(x+4\right)^2=-4$$  

• $$\pm2i$$  

• $$\pm6i$$  

• $$-4\pm2i$$  

• $$\pm2$$  

Multiple Choice

What are the values of x for the equation shown?

$$\left(x+4\right)^2=5$$  

• $$\pm\sqrt[]{5}$$  

• $$-9\ and-1$$  

• 2.236  

• $$\pm2$$  

Multiple Choice

Solve $$\left(5x-7\right)^2=0$$  

• $$\pm\frac{7}{5}$$  

• $$\frac{7}{5}$$  

• $$7\pm\sqrt[]{0}$$  

• $$5\pm\sqrt[]{7}$$