Discriminat
And Roots
And Roots
What is a discriminant?
The discriminant is the part of the quadratic formula under the square root, b^2 - 4ac, and is used to determine the nature of the roots for a quadratic equation.
Factor:
X^2 + 5x + 6
(x + 2)(x + 3)
Who is the NBA's all-time leading scorer?
LeBron James
Factor completely
X2+7X+10
(X+2)(X+5)
Where is Mount Everest located?
In the Himalayas, on the border between Nepal and Tibet (China)
Use the discriminant to determine the nature of the roots for the quadratic equation
-2x2+3x +8 =0
b2 - 4ac = 73
Since the value of the discriminant is positive, there are two distinct real roots.
What is the value of pi to 5 decimal places?
3. 14159
This is the completed square form of the equation
x^2 + 8x + 16
What is (x+4)(x+4)
Solve this factored equation
2(X-4)(7-2X)
X=4, X=7/2
A number multiplied by 3 more than itself is 40. What is the number?
x= 5, x= -8
Cows produce 3% less milk when listening to what kind of music?
Country
Factor:
2x^2 + 9x + 4
2x^2 + 8x + x + 4
= 2x(x + 4) + 1(x + 4)
= (2x + 1)(x + 4)
To solve x^2 - 10x +25 = 0 by completing the square, this is the solution
What is x=5?
Solve this quadratic equation by factoring
3w2+28w+9=0
w=9, x=1/3
The length of a rectangle is 2 meters more than its width. The area is 48 square meters. What is the width?
x= 6 (width), x+2=8 (length)
Use the discriminant to determine the nature of the roots for the quadratic equation
1/4x2-3x+9=0
b2 - 4ac = 0
Since the value of the discriminant is zero, there is one distinct real root, or two equal real roots.
Factor:
6x^2 + 12x + 6
6(x^2 + 2x + 1)
= 6(x + 1)(x + 1)
= 6(x + 1)^2
This is the completed square form of x^2 +4x +4
(x+2)^2
Solve this quadratic equation by completing the square
0.2x2+0.12x-11=0
x=-7.7, x=7.1
A ball is thrown upward from the ground with the equation h=−5t^2 +20t, where h is the height in meters after tt seconds. When does it hit the ground?
t= 0s, t= 4s
Use the discriminant to determine the nature of the roots for the quadratic equation
3x2 + 4x +4/3= 0
b2- 4ac = 0
Since the value of the discriminant is zero , there is one distinct real root, or two equal real roots.
Factor:
6x^2 + 11x + 3
6x^2 + 9x + 2x + 3
= 3x(2x + 3) + 1(2x + 3)
= (3x + 1)(2x + 3)
Solve 3^2+12x−6=0 by completing the square
x =-2 +/- √6
Name at least 4 of the Seven Wonders of the World
what is the name of the largest desert in Asia?
The Gobi Desert