Solving Quadratics & Imaginary Numbers

The Fundamental Theorem of Algebra states that a quadratic equation must:

• have fewer than 2 solutions

• have exactly 2 solutions

• have more than 2 solutions

• have 2 real solutions

The graph of a quadratic function takes the shape of:

• a circle

• a parabola

• a straight line

• a flat line

Which of the following is a quadratic equation in standard form?

• $2x^2-3=4x$

• $4x-3=0$

• $2x^2+4x-2=0$

• $x^2=5x+2$

Which of the following radical terms will simplify to  $2\sqrt{6}$  ?

•  $\sqrt{12}$  

•  $\sqrt{24}$  

•  $\sqrt{26}$  

•  $\sqrt{48}$  

Simplify

 $\sqrt{245}$  

•  $15$  

•  $5\sqrt{7}$  

•  $7\sqrt{5}$  

•  $\sqrt{245}$  (already simplified)

Solve:  $2x^2-19x+35=0$  

•  $\frac{5}{2},7$  

•  $-\frac{5}{2},\ -7$  

• 0

•  $\frac{19\pm9}{4}$  

What kind of solutions, and how many, will the following equation have:  $5x^2-2x-13=0$  

• 2 real

• 1 real

• 1 real, 1 non-real

• 2 non-real

Solve:  $3x^2+8x=5$  

•  $\frac{-4\pm\sqrt{31}}{3}$  

•  $\frac{-8\pm2\sqrt{31}}{6}$  

•  $\frac{-8\pm\sqrt{124}}{6}$  

•  $\frac{-8\pm\sqrt{31}}{3}$  

Solve:  $3x^2+7x+7=0$  

•  $\frac{2\pm4i\sqrt{2}}{3}$  

•  $\frac{5\pm i\sqrt{71}}{8}$  

•  $\frac{-7\pm i\sqrt{35}}{6}$  

•  $\frac{2\pm2\sqrt{10}}{3}$  

Solve:  $11x^2+5=x$  

•  $\frac{1\pm i\sqrt{219}}{22}$  

•  $\frac{1\pm\sqrt{221}}{22}$  

•  $\frac{-1\pm i\sqrt{239}}{10}$  

•  $\frac{\pm i\sqrt{70}}{10}$