Differentation: x intercept

Mar 2008
242
8
i have the problem how to calculate the x intercept for the attach graph. please refer graph.jpg

here i also attach my calculation how to get x intercept. it is very different from the solution.

hope some one con comment on it

tq(Crying)
 

Attachments

Mar 2010
280
122
\(\displaystyle x^2-x^3+8=0\)- this is cubic equation.
Your solution is incorrect.
It is solved more complicated than quadratic equation.
 
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dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
i have the problem how to calculate the x intercept for the attach graph. please refer graph.jpg

here i also attach my calculation how to get x intercept. it is very different from the solution.

hope some one con comment on it

tq(Crying)
\(\displaystyle y=\frac{x^2(1-x)+8}{1-x}\to 0=x^2(1-x)+8\to -x^3+x^2+8=0\)

You can use Des Cartes Rule of Sign.

(+) 1
(-) 0
(i) 2

Answer isn't rational.
 
Last edited:
Mar 2008
242
8
\(\displaystyle y=\frac{x^2(1-x)+8}{1-x}\to 0=x^2(1-x)+8\to -x^3+x^2+8=0\)

You can use Des Cartes Rule of Sign and synthetic division to solve.

(+) 1
(-) 0
(i) 2
why not we just factorize
\(\displaystyle
-x^3+x^2+8=0
\)
 

dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
\(\displaystyle a=-1, b=1, c=0,\) and \(\displaystyle d=8\)

\(\displaystyle x=\sqrt[3]{\left(\frac{-b^3}{27a^3}+\frac{bc}{6a^2}-\frac{d}{2a}\right)+\sqrt{\left(\frac{-b^3}{27a^3}+\frac{bc}{6a^2}-\frac{d}{2a}\right)^2+\left(\frac{c}{3a}-\frac{b^2}{9a^2}\right)^3}}\)\(\displaystyle +\sqrt[3]{\left(\frac{-b^3}{27a^3}+\frac{bc}{6a^2}-\frac{d}{2a}\right)-\sqrt{\left(\frac{-b^3}{27a^3}+\frac{bc}{6a^2}-\frac{d}{2a}\right)^2+\left(\frac{c}{3a}-\frac{b^2}{9a^2}\right)^3}}\)\(\displaystyle -\frac{b}{3a}\)
 
Last edited:
Mar 2008
242
8
\(\displaystyle a=-1, b=1, c=0,\) and \(\displaystyle d=8\)

\(\displaystyle x=\sqrt[3]{\left(\frac{-b^3}{27a^3}+\frac{bc}{6a^2}-\frac{d}{2a}\right)+\sqrt{\left(\frac{-b^3}{27a^3}+\frac{bc}{6a^2}-\frac{d}{2a}\right)^2+\left(\frac{c}{3a}-\frac{b^2}{9a^2}\right)^2}}\)\(\displaystyle +\sqrt[3]{\left(\frac{-b^3}{27a^3}+\frac{bc}{6a^2}-\frac{d}{2a}\right)+\sqrt{\left(\frac{-b^3}{27a^3}+\frac{bc}{6a^2}-\frac{d}{2a}\right)^2+\left(\frac{c}{3a}-\frac{b^2}{9a^2}\right)^2}}\)\(\displaystyle -\frac{b}{3a}\)
tq for the formulae ..so what is name of the formulae, i try to search it. is it Des Cartes Rule of Sign??

according to your post before, the answer is
(+) 1
(-) 0
(i) 2

but according to attached graph, it not exactly root is 2

ok i think i need to key in the a=-1, b=1, c=0 & d=8, into the above equation??
 

dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
(+) 1
(-) 0
(i) 2

but according to attached graph, it not exactly root is 2
That says there is 1 positive solution and 2 imaginary.

Formula Cardano.