anonymous
  • anonymous
what are the real or imaginary solutions of the polynomial equation 125x^3 + 343 = 0
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
factor the sum of two cubes.
watchmath
  • watchmath
\((5x)^3+9^3=0\) \((5x)^3=-9^3\) \(5x=-9\) \(x=-9/5\)
anonymous
  • anonymous
\[(5x^3)+7^3=(5x+7)((5x)^2-5x\times 7 + 7^2)\]

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watchmath
  • watchmath
oh I forgot the imaginary ...
anonymous
  • anonymous
and cube root of 343 is 7 not 9 i think
watchmath
  • watchmath
yes :) you were right sattelite. So ignore my answer :D.
anonymous
  • anonymous
i am using \[a^3+b^3=(a+b)(a^2-ab+b^2)\]
dumbcow
  • dumbcow
-7/5 7^3 = 343
watchmath
  • watchmath
we need two more complex solutions dumbcow
anonymous
  • anonymous
so we have \[(5x+7)(25x^2-35x+49)=0\] \[5x+7=0\] \[x=-\frac{7}{5}\]
anonymous
  • anonymous
and the other two you find using the quadratic formula.
anonymous
  • anonymous
i will write them out if you like
anonymous
  • anonymous
\[\frac{35\pm \sqrt{35^2-4\times 25\times 49}}{2\times 25}\] \[\frac{35\pm \sqrt{-3675}}{50}\] \[\frac{35\pm 5\sqrt{147}i}{50}\] \[\frac{7\pm \sqrt{147}i}{10}\]

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