Discriminant
What does the discriminant tell you?
The number of real solutions.
x^2+2x-24=0
x=-6, x=4
If you are measuring a rectangular park with an area of 72 square yards and the length is 2 more than four times the width, what is the length and width of the park?
L=18, W=4
An object is thrown vertically from an initial height of 3 meters with a speed of 14 meters per second and the gravitational force accelerates and decelerates it at 9.1 meters per second squared, after what time does the object reach the ground at 0 meters?
5t^2-14t-3=0 or 3 seconds.
What would the discriminant have to be in order for there to be one real solution?
0
x^2+9x+14=0
x=7, x=2
If you are trying to find out the length and width of a rectangular helicopter pad with an area of 64 square units and a perimeter of 40 units, how big would the dimensions be?
L=16, W=4 or L=4, W=16
An object is dropped from a height of 20 meters and the gravitational force (g) accelerates the object at 9.1 meters per seconds squared (plus the air friction is negligible in this situation), what is the speed of the object when it hits the ground?
V^2-2gh=0 which is equal to 20 meters per second
If you were given a quadratic equation and the discriminant was equal to 134, how many real solutions would there be?
2
x^2+65x-678=0
x=-13, x=-52
If you are building a fence around a rectangular garden and the area of the garden is 36 units squared, how much is the length and the width of the garden if the length is 5 units greater than the width?
w=4, L=9
If there are two resistors that are in a parallel connection and one of them has a resistance 3 units greater than the other, what is the resistance of each resistor if the resulting resistance is 10 units?
One resistor is 18.6 and the other is 21.6.
Who was the first to acknowledge the value of the discriminant?
Muhammad Ibn Musa Al-Khwarizmi
3x^2+288x+6045=0
x=-65, x=-31
If you wanted to fit a frame over a photo that is 6 by 8 inches and the frame is an area of 32 square inches, how thick is the frame?
The distance between point A and point B is 30 miles. If you are driving a boat between these two points and the current is 3mph, what would be the boat's speed (excluding the boost or penalty from the current) in order to make a round trip in 4 hours assuming you were traveling the same speed all throughout?
The square root of 54.