1 / 4

Ex. 6 Use the discriminant to determine the number of real solutions of the quadratic equation.

Discriminant: b 2 – 4ac used to determine the number of real solutions for quad. Equation 1) if discriminant is POSITIVE, two different solutions 2) if discriminant is ZERO, one repeated solution 3) if discriminat is NEGATIVE, no real solutions, no x-int.

amena-ayala
Download Presentation

Ex. 6 Use the discriminant to determine the number of real solutions of the quadratic equation.

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Discriminant: b2 – 4ac used to determine the number of real solutions for quad. Equation 1) if discriminant is POSITIVE, two different solutions 2) if discriminant is ZERO, one repeated solution 3) if discriminat is NEGATIVE, no real solutions, no x-int. Ex. 6 Use the discriminant to determine the number of real solutions of the quadratic equation. a. x2 + 4x – 32 = 0 b. 2x2 + 5x + 8 = 0 c. 2x2 + 12x +18 = 0 144, so 2 solutions -39, so no real sol. 0, so 1 sol.

  2. Ex. 7 A room is 3 ft longer than it is wide and has an area of 154 ft2. Find the dimensions of the room. w w(w + 3) = 154 w + 3 w2 + 3w – 154 = 0 (w – 11)(w + 14) = 0 width = 11 ft and length = 14 ft w = 11, - 14 Ex. 8 A construction worker on the 24th floor of a building (235 ft above ground) accidentally drops a wrench and yells “Look out below!” Could a person at ground level hear this warning in time to get out of the way? (speed of sound is about 1100 ft/sec) s = - 16t2 + vot + so t2 = 235/16 t = 3.83 sec 0 = -16t2 + 0t + 235 16t2 = 235 Person hears warning less one second after wrench is dropped. Plenty-o-time.

  3. Ex. 9 From 2000 to 2007, the estimated number of Internet users, I (in millions) in the US can be modeled by the quadratic equation I = -1.163t2 + 17.19t + 125.9 0 ≤ t ≤ 7 In which year will the number of users reach or surpass 180 million? I = -1.163t2 + 17.19t + 125.9 180 = -1.163t2 + 17.19t + 125.9 0 = -1.163t2 + 17.19t – 54.1 Since it must be between 2000 and 2007, the 10.2 does not count so it must be 4.5 or during the 2004 year.

  4. Ex. 10 An L-shaped sidewalk was constructed so that the length of one sidewalk forming the L was twice as long as the other side. The length of the diagonal sidewalk that connects the other two is 32 feet long. How many feet does a person save by walking on the diagonal sidewalk? x2 + (2x)2= 322 x2 + 4x2 = 1024 2x 32 5x2 = 1024 x2 = 204.8 x = 14.3 ft x so distance around the “L” is 3(14.3) = 42.9 ft Someone saved 10 ft going diagonally.

More Related