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Problem Solving Using the Discriminant

9.5. Problem Solving Using the Discriminant. Quadratic Equation:. 2. Discriminant: b 2 -4ac. If b 2 -4ac is positive, then 2 solutions If b 2 -4ac is 0, then 1 solution If b 2 -4ac is negative, then no solution.

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Problem Solving Using the Discriminant

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  1. 9.5 Problem Solving Using the Discriminant

  2. Quadratic Equation: 2 Discriminant: b2-4ac Ifb2-4ac is positive, then 2 solutions Ifb2-4ac is 0, then 1 solution If b2-4ac is negative, then no solution

  3. 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=0 x2-7x+16=0 b2-4ac b2-4ac 42-4(3)(-5) (-7)2-4(1)(16) 16+60 49-64 -15 76 No Solution 2 Solutions

  4. 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+0 0=-16t2+30t-15

  5. Find discriminant to see if there is a solution before solving. b2-4ac 302-4(-16)(-15) 900-960 -60 NO SOLUTION You must throw it harder

  6. 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?

  7. 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

  8. 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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