POLYNOMIALS - ROOTS
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Show that the equation x^3-14x+1=3 has exactly three solutions in the interval [-5,5] using the fact that a polynomial of order three has at most three roots.
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26-Feb-2015 at 6:00 am.
--------------------------------Show that the equation x^3-14x+1=3 has exactly three solutions in the interval [-5,5] using the fact that a polynomial of order three has at most three roots.
| LET US CHECK F[X] IN THE INTERVAL | |||||||||
| X | F[X] | ||||||||
| -5 | -57 | ||||||||
| -4 | -10 | ||||||||
| -3 | 13 | ||||||||
| -2 | 18 | ||||||||
| -1 | 11 | ||||||||
| 0 | -2 | ||||||||
| 1 | -15 | ||||||||
| 2 | -22 | ||||||||
| 3 | -17 | ||||||||
| 4 | 6 | ||||||||
| 5 | 53 | ||||||||
| F[X] BEING A POLYNOMIAL IS CONTINUOUS IN THE INTERVAL | |||||||||
| WE FIND THAT IT CHANGES SIGN AROUND 3 POINTS IN THE GIVEN INTERVAL .. | |||||||||
| [-4 , -3] …………….;……………..[-1,0]……………. ;[3,4] | |||||||||
| HENCE THERE ARE 3 ZEROS OR 3 ROOTS TO THE POLYNOMIAL IN THIS INTERVAL | |||||||||
| BUT | |||||||||
| a polynomial of order three | has at most three roots. | ||||||||
| SO THE POLYNOMIAL HAS GOT EXACTLY 3 SOLUTIONS IN THE GIVEN INTERVAL | |||||||||
posted by mathsmanagementcommonsense at 8:42 PM
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