1 / 7

When ax 2 + bx + c is Always Positive or Always Negative

When ax 2 + bx + c is Always Positive or Always Negative. Example 1. Since a<o and discriminant <0 , the graph lies below the x-axis. Hence, the function f(x) is always negative for all real values of x. Example 2 Prove that 2 x 2 – 3 x + 4 is always positive for

hume
Download Presentation

When ax 2 + bx + c is Always Positive or Always Negative

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. When ax2 + bx+ c is Always Positive or Always Negative

  2. Example 1 Since a<o and discriminant <0, the graph lies below the x-axis Hence, the function f(x) is always negative for all real values of x.

  3. Example 2 • Prove that 2x2 – 3x + 4 is always positive for • all real values of x.

  4. Example 3 • Show that 2kx – x2 – k2 – 3 is always negative • for all real values of k.

  5. Example 4 Find the range of values of k for which 2x2 + x + k is always positive for all real values of x. • Note: The phrase “for all real values of x” does NOTrefer to the equation having real roots. Also, the term “positive” does NOT imply that the discriminant is positive.

  6. Example 5[J01/I9ii] Find the range of values of c for which x2 + 7x – 9 > 8x + c, for all values of x. [3]

  7. Example 6 [J84/I/13a] Find the range of values of k for which 8 – 3x – x2k for all real values of x.

More Related