Reducing Radicals
Reduce sqrt27 if we can write it as sqrt(9*3)
3 sqrt3
I found the discriminant of 3x^2-x+6=0 to be -71. How many solutions does this equation have?
0, no solutions
Solve the following quadratic equation x2 = 16
x=+-4
What is the quadratic formula?
x =( -b pm sqrt(b^2 - 4ac)) /(2a)
Provide an example of an irrational number.
Pi or the square root of any non perfect square such as sqrt2
sqrt144
12
Find the discriminant of 3x^2+8x+2=0 using b^2-4ac .
40
Solve the following quadratic equation : x2 = -9
{No solution}
Solve the following quadratic equation by using the quadratic formula: x2 + 6x + 5 = 0
x = -1, x = -5
What year was the quadratic formula invented (the one we use today)?
Closest guess wins the points!
1594
sqrt72
6sqrt2
Find the discriminant of x^2-8x+16=0 using b^2-4ac .
0
Solve the following quadratic equation by completing the square: x2 - 2 = 23
x=+-5
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
What is standard form of a quadratic equation?
ax^2+bx+c=0
sqrt175
5sqrt7
Find the discriminant of 2x^2+10x-5=0 using b^2-4ac AND determine how many solutions the equation has.
140, 2 solutions
Solve the following quadratic equation.
4x^2-16=48
x=+-4
Solve the following quadratic equation by using the quadratic formula: 2x2 + 9x + 4 = 0
{-1/2, -4}
What is root(3)(512)
8, since 8x8x8=512
sqrt180
6sqrt5
Find the discriminant of -x^2+12x-36=0 using b^2-4ac AND determine how many solutions the equation has.
0, 1 solution
Solve the following quadratic equation:
-2x2 -5 = 13
No Solution
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
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"