1 / 15

How many real solutions does x 2 -9x+8=0 have?

Can you predict whether a quadratic equation will have two real solutions, one real solution, or no real solutions?. How many real solutions does x 2 -9x+8=0 have?.

ivie
Download Presentation

How many real solutions does x 2 -9x+8=0 have?

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. Can you predict whether a quadratic equation will have two real solutions, one real solution, or no real solutions? How many real solutions does x2-9x+8=0 have?

  2. In this lesson you will learn how to determine if a quadratic function has two real roots, one real root, or no real roots by looking at the discriminant.

  3. Also called roots Quadratic equation 0=ax2+bx+c A quadratic equation can have two solutions. One way to find them is with the quadratic formula.

  4. Remember to be careful with signs. x2-9x+8=0

  5. The discriminant of a polynomial gives information about its roots. is the discriminant

  6. We have three different cases when we take square roots. √50= 5√2 , -5√2 Positive number √0=0 Zero √-16= 4i, -4i Negative number

  7. If the discriminant is… A Positive number The quadratic equation has 2 DISTINCT real solutions A graph of the function has 2 DISTINCT x-intercepts

  8. If the discriminant is… Zero The quadratic equation has 1 DISTINCT real solution A graph of the function has 1 DISTINCT x-intercept

  9. If the discriminant is… A negative number The quadratic equation has No real solutions A graph of the function has no x-intercepts

  10. x2-9x+8=0 c=8 a=1 b=-9 1 (-9)2 -4(1)(8) 81 – 32 = 49 Discriminant is POSITIVE We have two distinct real roots.

  11. Since the discriminant of x2-9x+8 is POSITIVE, the graph of y=x2-9x+8 shows two x-intercepts

  12. In this lesson you learned how to determine if a quadratic function has two real roots, one real root, or no real roots by looking at the discriminant.

  13. What type of solutions does a quadratic with a discriminant of 25 have?

  14. Draw a rough sketch of a parabola given the following discriminant values. • 0, -49, 100, 17

  15. What types of roots would a quadratic equation have if your discriminant was -76? Describe the roots of the quadratic function y=x2-4x+2?

More Related