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.
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Polynomials and Quadratics Homework Help?
Started by camieac, Apr 20 2011 02:03 PM
1 reply to this topic
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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
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=-=-=
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