Quadratic Formula & Complex Numbers

Desean begins to use the quadratic formula to solve the following equation.

 $x^2-3x=9$  

Which expression shows a step in solving the above equation?

•  $\frac{3\pm\sqrt{45}}{2}$  

•  $\frac{-3\pm\sqrt{45}}{2}$  

•  $\frac{3\pm\sqrt{-27}}{2}$  

•  $\frac{-3\pm\sqrt{-27}}{2}$  

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.4

Look at the equation below.

 $x^2+2x-5=2$  

Which values of x satisfy the equation? Write your answers in simplest radical form.

•  $-1\pm2\sqrt{2}$  

•  $1\pm2\sqrt{2}$  

•  $-1\pm2i\sqrt{2}$  

•  $1\pm2i\sqrt{2}$  

Tags

CCSS.HSA.REI.B.4

What are the solutions to following equation? Write your answers in simplest radical form.

 $2x^2-x+1=0$  

•  $\frac{1}{4}-\frac{\sqrt{5}}{4}\ and\ \frac{1}{4}+\frac{\sqrt{5}}{4}$  

•  $\frac{1}{4}-\frac{\sqrt{7}}{4}\ and\ \frac{1}{4}+\frac{\sqrt{7}}{4}$  

•  $\frac{1}{4}-\left(\frac{\sqrt{7}}{4}\right)i\ and\ \frac{1}{4}+\left(\frac{\sqrt{7}}{4}\right)i$  

•  $\frac{1}{4}-\left(\frac{\sqrt{5}}{4}\right)i\ and\ \frac{1}{4}+\left(\frac{\sqrt{5}}{4}\right)i$  

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.4

CCSS.HSN.CN.A.1

CCSS.HSN.CN.A.2

Look at the equation below.

 $x^2+5x+7=0$  

What are the solutions of the equation? Write your answers in simplest radical form.

•  $\frac{-5\pm\sqrt{3}}{2}$  

•  $\frac{-5\pm i\sqrt{3}}{2}$  

•  $\frac{-5\pm\sqrt{53}}{2}$  

•  $\frac{-5\pm i\sqrt{53}}{2}$  

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.4

CCSS.HSN.CN.C.7

Solve the following equation. Write your answers in simplest radical form.

 $x^2+10x+35=0$  

•  $-5\pm2i\sqrt{5}$  

•  $-5\pm i\sqrt{5}$  

•  $-5\pm2i\sqrt{10}$  

•  $-5\pm i\sqrt{10}$  

Tags

CCSS.HSA.REI.B.4

What are the solutions to the following quadratic?

 $7x^2+x=4$  

Select all that apply.

•  $x=-0.831$  
  

•  $x=1.264$  

•  $x=0.688$  

•  $-0.264$  

•  $x=1.883$  

Tags

CCSS.HSA.REI.B.4

What is the value of the expression below?

 $8\left(5-3i\right)+i\left(3+2i\right)$  

•  $42-21i$  

•  $38-2i$  

•  $42+27i$  

•  $40-19i$  

Tags

CCSS.HSN.CN.A.1

CCSS.HSN.CN.A.2

What is the value of the expression below?

 $10i\left(-2+5i\right)$  

•  $-20i+50$  

•  $8i+15$  

•  $30i$  

•  $-20i-50$  

Tags

CCSS.HSN.CN.A.1

CCSS.HSN.CN.A.2

What is the value of the expression below?

 $\left(i+3\right)^2$  

•  $6i+8$  

•  $8$  

•  $3i+10$  

•  $9i+10$  

Tags

CCSS.HSA.APR.C.5

CCSS.HSA.SSE.A.2

CCSS.HSN.CN.A.1

CCSS.HSN.CN.A.2

Does the following expression have a real or imaginary solution?

 $5i\left(-6i^2\right)$  

• Real

• Imaginary

Tags

CCSS.HSN.CN.A.1

CCSS.HSN.CN.A.2