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Question 35763: please help! I am so lost and my algebra final is due in 9 hours!!!
x^4+2x^3-4x-4=0
I am supposed to find the positive roots to an accuracy of .1 using bisection. There is only one example in the book and that is for a 2nd degree poly. If anyone can help me with in the next few hours that would be great. Thank you!!
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! please help! I am so lost and my algebra final is due in 9 hours!!!
LET.....F(X)=x^4+2x^3-4x-4=0
I am supposed to find the positive roots to an accuracy of .1 using bisection. There is only one example in the book and that is for a 2nd degree poly. If anyone can help me with in the next few hours that would be great. Thank you!!
THERE IS ONLY ONE CHANGE IN SIGN FROM +2 TO -4 ..SO THERE CAN BE ONLY 1 POSITIVE ROOT
IF RATIONAL IT SHOULD BE A FACTOR OF 4...THAT IS 1,2,OR 4..NONE OF WHICH ARE OK.
F(1)=1+2-4-4=-5
F(2)=2^4+2*2^3-4*2-4=16+16-8-4=20...HENCE ROOT IS IRRATIONAL AND IS BETWEEN 1 & 2.
AS F(1) AND F(2) ARE OF DIFFERENT SIGNS,THERE MUST BE A ZERO VALUE BETWEEN THEM.
LET US TRY FACTORISATION BY DIVIDING THE TERMS
F(X)=(X^4-4)+2X(X^2-2)=0
=(X^2+2)(X^2-2)+2X(X^2-2)=0
(X^2-2)(X^2+2+2X)=0
HENCE X^2-2=0...OR...X^2=2...OR ....X=SQRT(2)=1.4142
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