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help-me-to-find-the-roots-of-x-5-5x-4-20x-3-60x-2-120x-120-0-




Question Number 141781 by gsk2684 last updated on 23/May/21
help me to find the roots of   x^5 +5x^4 +20x^3 +60x^2 +120x+120=0?
$${help}\:{me}\:{to}\:{find}\:{the}\:{roots}\:{of}\: \\ $$$${x}^{\mathrm{5}} +\mathrm{5}{x}^{\mathrm{4}} +\mathrm{20}{x}^{\mathrm{3}} +\mathrm{60}{x}^{\mathrm{2}} +\mathrm{120}{x}+\mathrm{120}=\mathrm{0}? \\ $$
Commented by MJS_new last updated on 23/May/21
in this case only approximation is possible
$$\mathrm{in}\:\mathrm{this}\:\mathrm{case}\:\mathrm{only}\:\mathrm{approximation}\:\mathrm{is}\:\mathrm{possible} \\ $$
Commented by MJS_new last updated on 23/May/21
I get  x≈−2.18060712404  no other real solutions
$$\mathrm{I}\:\mathrm{get} \\ $$$${x}\approx−\mathrm{2}.\mathrm{18060712404} \\ $$$$\mathrm{no}\:\mathrm{other}\:\mathrm{real}\:\mathrm{solutions} \\ $$

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