Warning: Illegal string offset 'html' in /home/hsn/public_html/forum/cache/skin_cache/cacheid_1/skin_topic.php on line 909

Warning: Cannot modify header information - headers already sent by (output started at /home/hsn/public_html/forum/cache/skin_cache/cacheid_1/skin_topic.php:909) in /home/hsn/public_html/forum/admin/sources/classes/output/formats/html/htmlOutput.php on line 114

Warning: Cannot modify header information - headers already sent by (output started at /home/hsn/public_html/forum/cache/skin_cache/cacheid_1/skin_topic.php:909) in /home/hsn/public_html/forum/admin/sources/classes/output/formats/html/htmlOutput.php on line 127

Warning: Cannot modify header information - headers already sent by (output started at /home/hsn/public_html/forum/cache/skin_cache/cacheid_1/skin_topic.php:909) in /home/hsn/public_html/forum/admin/sources/classes/output/formats/html/htmlOutput.php on line 136

Warning: Cannot modify header information - headers already sent by (output started at /home/hsn/public_html/forum/cache/skin_cache/cacheid_1/skin_topic.php:909) in /home/hsn/public_html/forum/admin/sources/classes/output/formats/html/htmlOutput.php on line 137

Warning: Cannot modify header information - headers already sent by (output started at /home/hsn/public_html/forum/cache/skin_cache/cacheid_1/skin_topic.php:909) in /home/hsn/public_html/forum/admin/sources/classes/output/formats/html/htmlOutput.php on line 141
Polynomials and Quadratics Homework Help? - HSN forum

Jump to content


Polynomials and Quadratics Homework Help?


1 reply to this topic

#1 camieac

    Newbie

  • Members
  • Pip
  • 1 posts
  • Gender:Male

Posted 20 April 2011 - 02:03 PM

Here's the question:

Show that x3 - 2x2 + 4x - 6 = 0 has a root between 1 and 2. Find the root correct to two decimal places.

#2 Marcus

    Site Swot

  • Members
  • PipPipPipPip
  • 147 posts
  • Location:Aberdeen
  • Interests:Guitar - Passed my grade 6 :D :D<br />Write computer programs - won Heriot-Watt programming challenge 2006 and 2007 :D<br />
  • Gender:Male

Posted 26 April 2011 - 11:53 AM

quite easy to show it has a root between 1 and 2

x3 - 2x2 + 4x - 6

let x=1
13 - (2)(12) + 4(1) - 6 = -3
let x=2
23 - (2)(22) + 4(2) - 6 =2

since polynomials are continuous functions (they don't have jumps or breaks), since at 1 it is below the x-axis and at 2 it is above the x-axis at some point in between it must have crossed it.

As for finding the root to 2 dp, the only way to do this in higher is trial and error, start at a number say 1.5 substitute it in if negative increase the number, if positive decrease it.

[Answer should be 1.71 as 1.71 is negative but 1.715 is positive so root has to be between them, which rounded to 2 dp, is always 1.71]

Hope this helps
=-=-=Marcus=-=-=





1 user(s) are reading this topic

0 members, 1 guests, 0 anonymous users