3.8 Complex Quadratic Roots

Are the roots of the function 

 $f\left(x\right)=3x^2-3x+3$ 
real or imaginary?

• Real Roots

• Imaginary Roots

• Impossible to tell

• Both

Solve:
 $x^2-8x-20=0$  

•  $x=\left\{10,-2\right\}$  

•  $x=\left\{-10,\ 2\right\}$  
  

•  $x=\left\{\frac{8\pm\sqrt{12}}{2}\right\}$  

•  $x=\left\{6,1\right\}$  

Find the roots:  $x^2-4x+5$  

• x = {-4, -1}

• x = {-1, -4}

• x = {2 + i, 2 - i}

• x = {-2 + i, -2 - i}

Find the roots:
 $x^{2\ }+6x+13$ 

• x = {-3 + 2i, -3 - 2i}

• x = {7, 6}

• x = 2 ± i√3

• No solution

Solve for x:
 $x^2-5x+8=0$ 

•  $x=\left\{\frac{-5\pm i\sqrt{7}}{2}\right\}$ 

•  $x=\left\{\frac{5\pm i\sqrt{7}}{2}\right\}$  

•  $x=\left\{\frac{8\pm i\sqrt{7}}{2}\right\}$  

•  $x=\left\{\frac{5\pm\sqrt{57}}{2}\right\}$  

Solve for x:
 $x^2-3x+10=0$ 

•  $x=\left\{-3\pm i\sqrt{31}\right\}$ 

•  $x=\left\{\frac{3\pm\sqrt{49}}{2}\right\}$  
  

•  $x=\left\{5,\ -2\right\}$  

•  $x=\left\{\frac{3\pm i\sqrt{31}}{2}\right\}$  

Solve for x: 3x² - 6x + 6 = 0

• x = 1 ± i

• x = 3, -6

• x = 4.8, 2.7

• Undefined

Solve:
 $x^2+6x+27=0$  

•  $3\pm\sqrt{18}$  

•  $3\pm i\sqrt{18}$  

•  $-3\pm i\sqrt{18}$  

•  $-3\pm\sqrt{18}$  

Solve the equation $3x^2+96=0$  

•  $\pm4\sqrt{2}$  

•  $\pm4i\sqrt{2}$  

•  $2i\sqrt{4}$  

•  $\pm2\sqrt{4}$  

Solve the equation $x^2+8x+20=0$  

•  $-4\pm2i$  

•  $2i\pm4$  

•  $-2\pm4i$  

•  $3\pm2i$