Solving Quadratic Equations

Reducing Radicals

100

 Reduce sqrt27 if we can write it as sqrt(9*3) 

3 sqrt3

200

sqrt144

12

300

sqrt72

6sqrt2

400

sqrt175

5sqrt7

500

sqrt180

6sqrt5

The Discriminant

100

I found the discriminant of  3x^2-x+6=0 to be -71. How many solutions does this equation have?

0, no solutions

200

Find the discriminant of  3x^2+8x+2=0 using  b^2-4ac .

40

300

Find the discriminant of  x^2-8x+16=0 using  b^2-4ac .

0

400

Find the discriminant of  2x^2+10x-5=0 using  b^2-4ac AND determine how many solutions the equation has.

140, 2 solutions

500

Find the discriminant of  -x^2+12x-36=0 using  b^2-4ac AND determine how many solutions the equation has.

0, 1 solution

Taking Square Roots

100

Solve the following quadratic equation  x²  = 16

x=+-4

200

Solve the following quadratic equation : x²  = -9

 {No solution}

300

Solve the following quadratic equation by completing the square: x² - 2 = 23

x=+-5

400

Solve the following quadratic equation. 

4x^2-16=48

x=+-4

500

Solve the following quadratic equation: 

-2x² -5 = 13

No Solution

Quadratic Formula

100

What is the quadratic formula?

x =( -b pm sqrt(b^2 - 4ac)) /(2a)

200

Solve the following quadratic equation by using the quadratic formula: x² + 6x + 5 = 0

x = -1, x = -5

300

Solve the following quadratic equation by using the quadratic formula. x² - 9x + 6 = 0

 (9 pm sqrt(57))/2 

x=8.3 & x=0.7

400

Solve the following quadratic equation by using the quadratic formula: 2x² + 9x + 4 = 0

{-1/2, -4}

500

Solve the following quadratic equation by using the quadratic formula (nearest tenth): 

4x² - 17x =-12 

Hint: Move all three terms to the same side of the = before using the formula!

 x = (17 pm sqrt(97))/8 

x=3.4 & x=0.9

Math Trivia

100

Provide an example of an irrational number.

Pi or the square root of any non perfect square such as  sqrt2 

200

What year was the quadratic formula invented (the one we use today)?

Closest guess wins the points!

1594

300

What is standard form of a quadratic equation?

ax^2+bx+c=0

400

What is  root(3)(512) 

8, since 8x8x8=512

500

Al-Khwarizmi famously solved a quadratic equation in his book Al-Jabr around 820 AD. What method did he use?

Completing the Square

Fun fact -> Al-Jabr is where the word Algebra comes from; it means "the reunion of broken pieces"