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 August 27th, 2017, 10:52 PM #1 Newbie   Joined: Aug 2017 From: America Posts: 5 Thanks: 0 finding x in an equation x^4+5x^3+50x^2-140x+168=0
 August 27th, 2017, 11:51 PM #2 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,422 Thanks: 484 Math Focus: Yet to find out. ...
 August 28th, 2017, 02:38 AM #3 Newbie   Joined: Jul 2017 From: Iraq Posts: 18 Thanks: 0 Newton-Raphson Best solution is to use Newton-Raphson Numerical method to evaluate the given function. Last edited by skipjack; August 28th, 2017 at 09:32 AM.
 August 28th, 2017, 04:56 AM #4 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,642 Thanks: 960 Math Focus: Elementary mathematics and beyond That equation has no real roots.
 August 28th, 2017, 05:05 AM #5 Math Team   Joined: Jan 2015 From: Alabama Posts: 2,829 Thanks: 753
 August 28th, 2017, 06:13 AM #6 Member   Joined: May 2017 From: Russia Posts: 33 Thanks: 4 One could use CAS Maxima. Code: algexact: true; tex(algsys([x^4+5*x^3+50*x^2-140*x+168],[x])); $\displaystyle \left[ \left[ x={{\sqrt{{{5985}\over{2\,\sqrt{{{26464-975\,\left({{ 301400}\over{27}}+{{56\,\sqrt{782431}\,i}\over{3}} \right)^{{{1 }\over{3}}}+36\,\left({{301400}\over{27}}+ {{56\,\sqrt{782431}\,i }\over{3}}\right)^{{{2}\over{3}}}}\over{\left({{30 1400}\over{27}}+{{ 56\,\sqrt{782431}\,i}\over{3}}\right)^{{{1}\over{3 }}}}}}}}-\left({{ 301400}\over{27}}+ {{56\,\sqrt{782431}\,i}\over{3}}\right)^{{{1 }\over{3}}}-{{6616} \over{9\,\left({{301400}\over{27}}+{{56\,\sqrt{782 431}\,i}\over{3}}\right)^{{{1}\over{3}}}}}-{{325}\over{6}}} }\over{2}}+{{\sqrt{{{26464-975\,\left({{301400}\over{27}}+{{56\, \sqrt{782431}\,i}\over{3}}\right)^{{{1}\over{3}}}+ 36\,\left({{301400 }\over{27}}+{{56\,\sqrt{782431}\,i}\over{3}}\right )^{{{2}\over{3}}} }\over{\left({{301400}\over{27}}+{{56\,\sqrt{78243 1}\,i}\over{3}} \right)^{{{1}\over{3}}}}}}}\over{12}}-{{5}\over{4}} \right] , \left[ x=-{{\sqrt{{{5985}\over{2\,\sqrt{{{26464-975\,\left({{301400 }\over{27}}+{{56\,\sqrt{782431}\,i}\over{3}}\right )^{{{1}\over{3}}}+ 36\,\left({{301400}\over{27}}+{{56\,\sqrt{782431}\ ,i}\over{3}} \right)^{{{2}\over{3}}}}\over{\left({{301400}\over {27}}+{{56\,\sqrt{782431}\,i}\over{3}}\right)^{{{1 }\over{3}}}}}}}}-\left({{301400 }\over{27}}+{{56\,\sqrt{782431}\,i}\over{3}}\right )^{{{1}\over{3}}}- {{6616}\over{9\,\left({{301400}\over{27}}+ {{56\,\sqrt{782431}\,i }\over{3}}\right)^{{{1}\over{3}}}}}-{{325}\over{6}}}}\over{2}}+{{ \sqrt{{{26464-975\,\left({{301400}\over{27}}+ {{56\,\sqrt{782431}\,i }\over{3}}\right)^{{{1}\over{3}}}+36\,\left({{3014 00}\over{27}}+{{56 \,\sqrt{782431}\,i}\over{3}}\right)^{{{2}\over{3}} }}\over{\left({{ 301400}\over{27}}+ {{56\,\sqrt{782431}\,i}\over{3}}\right)^{{{1 }\over{3}}}}}}}\over{12}}-{{5}\over{4}} \right] , \left[ x={{\sqrt{ -{{5985}\over{2\,\sqrt{{{26464-975\,\left({{301400}\over{27}}+{{56\, \sqrt{782431}\,i}\over{3}}\right)^{{{1}\over{3}}}+ 36\,\left({{301400 }\over{27}}+ {{56\,\sqrt{782431}\,i}\over{3}}\right)^{{{2}\over {3}}} }\over{\left({{301400}\over{27}}+{{56\,\sqrt{78243 1}\,i}\over{3}} \right)^{{{1}\over{3}}}}}}}}-\left({{301400}\over{27}}+{{56\,\sqrt{782431}\,i}\ over{3}}\right)^{{{1}\over{3}}}-{{6616}\over{9\,\left({{ 301400}\over{27}}+{{56\,\sqrt{782431}\,i}\over{3}} \right)^{{{1 }\over{3}}}}}-{{325}\over{6}}}}\over{2}}-{{\sqrt{{{26464-975\,\left( {{301400}\over{27}}+{{56\,\sqrt{782431}\,i}\over{3 }}\right)^{{{1 }\over{3}}}+36\,\left({{301400}\over{27}}+ {{56\,\sqrt{782431}\,i }\over{3}}\right)^{{{2}\over{3}}}}\over{\left({{30 1400}\over{27}}+{{ 56\,\sqrt{782431}\,i}\over{3}}\right)^{{{1}\over{3 }}}}}}}\over{12}}- {{5}\over{4}} \right] , \left[ x=-{{\sqrt{-{{5985}\over{2\,\sqrt{{{ 26464-975\,\left({{301400}\over{27}}+{{56\,\sqrt{782431} \,i}\over{3 }}\right)^{{{1}\over{3}}}+36\,\left({{301400}\over {27}}+{{56\,\sqrt{782431}\,i}\over{3}}\right)^{{{2 }\over{3}}}}\over{\left({{301400 }\over{27}}+{{56\,\sqrt{782431}\,i}\over{3}}\right )^{{{1}\over{3}}} }}}}}-\left({{301400}\over{27}}+{{56\,\sqrt{782431}\,i}\ over{3}} \right)^{{{1}\over{3}}}-{{6616}\over{9\,\left({{301400}\over{27}}+{{ 56\,\sqrt{782431}\,i}\over{3}}\right)^{{{1}\over{3 }}}}}-{{325}\over{ 6}}}}\over{2}}-{{\sqrt{{{26464-975\,\left({{301400}\over{27}}+{{56\, \sqrt{782431}\,i}\over{3}}\right)^{{{1}\over{3}}}+ 36\,\left({{301400 }\over{27}}+{{56\,\sqrt{782431}\,i}\over{3}}\right )^{{{2}\over{3}}} }\over{\left({{301400}\over{27}}+{{56\,\sqrt{78243 1}\,i}\over{3}} \right)^{{{1}\over{3}}}}}}}\over{12}}-{{5}\over{4}} \right] \right]$ Last edited by skipjack; August 28th, 2017 at 09:58 AM.
 August 29th, 2017, 06:17 AM #7 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,927 Thanks: 718 Holy Maxima, Victor!! x^4 - 10x^3 + 35x^2 - 50x + 24 = 0 Try that one...
 August 29th, 2017, 06:24 AM #8 Member   Joined: May 2017 From: Russia Posts: 33 Thanks: 4 Code: factor(x^4 - 10*x^3 + 35*x^2 - 50*x + 24); $\displaystyle (x-4)(x-3)(x-2)(x-1)$
 August 29th, 2017, 06:35 AM #9 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,927 Thanks: 718 Aha! Thanks to me, your post this time is only 1 line Btw, should be (x - 1)(x - 2)(x - 3)(x - 4)
August 29th, 2017, 12:20 PM   #10
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 Originally Posted by Denis Holy Maxima...
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