Problem Solving Using the

Discriminant

Quadratic Equation:

a

acbbx

2

4

2

Discriminant: b2-4acIf b2-4ac is positive, then 2 solutions

If b2-4ac is 0, then 1 solution

If b2-4ac is negative, then no solution

If you find the discriminant, you can tell whether or not

you will have a solution.Find the discriminant and number of solutions for:

3x2+4x-5=0b2-4ac42-4(3)(-5)16+60

762 Solutions

x2-7x+16=0b2-4ac

(-7)2-4(1)(16)49-64-15

No Solution

Equations:Object dropped h=-16t2+s

Object thrown h=-16t2+vt+s

You are standing beneath a ledge that is 15 ft. high. If you throw a rope up at a

velocity of 30 ft/sec., will it reach the ledge?Which

equation?15=-16t2+30t+00=-16t2+30t-15

Find discriminant to see if there is a solution before

solving. b2-4ac302-4(-16)(-15)

900-960

-60NO SOLUTION

You must throw it harder

Try this one

• Rick is a firefighter and is leaning out a window on the eighth floor. He is trying to throw a grappling hook to a tenth-floor window that is 26 feet above him.

• Rick can throw the grappling hook with a maximum speed of 40 feet per second. Can he throw the grappling hook to the window above him?

Which formula do you need?

• h = -16t2 + vt + s• Plug in what you know and solve.• 26 = -16t2 + 40t + 0• 0 = -16t2 + 40t - 26• b2-4ac• 402 – 4(-16)(-26)• 1600 – 1664• -64

Answer:

• The discriminate is -64, so he cant throw it high enough.

• If he could throw it a little faster or if the window were a little closer, he could make it.