Problem Solving Using the Discriminant Quadratic Equation 2
Problem Solving Using the Discriminant
Quadratic Equation: 2 Discriminant: 2 b -4 ac If b 2 -4 ac is positive, then 2 solutions If b 2 -4 ac is 0, then 1 solution If b 2 -4 ac 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: 3 x 2+4 x-5=0 b 2 -4 ac 42 -4(3)(-5) 16+60 76 2 Solutions 2 x -7 x+16=0 b 2 -4 ac (-7)2 -4(1)(16) 49 -64 -15 No Solution
Equations: Object dropped h=-16 t 2+s Object thrown h=-16 t 2+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 2+30 t+0 15=-16 t equation? 0=-16 t 2+30 t-15
Find discriminant to see if there is a solution before solving. 2 b -4 ac 302 -4(-16)(-15) 900 -960 -60 NO 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 = -16 t 2 + vt + s Plug in what you know and solve. 26 = -16 t 2 + 40 t + 0 0 = -16 t 2 + 40 t - 26 b 2 -4 ac 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.
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