Quadratics with Complex Solutions

When you are solving for the roots/zeros of a quadratic function, which equation should you use?

• $D=b^2-4ac$

• $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

When you are solving for the amount of solutions, which equation should you use?

• $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

• $D=b^2-4ac$

How many solutions would a quadratic have if D > 0?

• 2 Complex Solutions

• 1 Real Solution

• 2 Real Solutions

How many solutions would a quadratic have if D = 0

• 2 Complex Solutions

• 1 Real Solution

• 2 Real Solutions

How many solutions would a quadratic have if D < 0?

• 2 Complex Solutions

• 1 Real Solution

• 2 Real Solutions

How many solutions does this equation have?

• 2 Real Solutions

• 1 Real Solution

• 2 Complex Solutions

Find the roots of the equation.

• $\left\{\frac{3+3i\sqrt{7}}{-4},\frac{3-3i\sqrt{7}}{-4}\right\}$

• $\left\{-3i\sqrt{7},3i\sqrt{7}\right\}$

• $\left\{-63,63\right\}$

How many roots does the following equation have:

 $2x^2+6x=11$  

• 2 Complex Solutions

• 1 Real Solution

• 2 Real Solutions

Find the roots of the following quadratics:

 $2x^2+6x=11$  

•  $\left\{\frac{11}{2},8\right\}$  

•  $\left\{-2\sqrt{31},\ -\sqrt{31}\right\}$  

•  $\left\{\frac{-3+\sqrt{31}}{2},\ \frac{-3-\sqrt{31}}{2}\right\}$  

• No Solutions

Find all roots for the following quadratic:

 $-3x^2-8$  

•  $\left\{\frac{3\sqrt{6}}{2}\right\}$  

•  $\left\{\frac{2i\sqrt{6}}{-3},\ \frac{2i\sqrt{6}}{3}\right\}$  

•  $\left\{-6,6\right\}$  

• No Solutions