Question

what are the real or imaginary solutions of the polynomial equation 125x^3 + 343 = 0

Answer 1

factor the sum of two cubes.

Answer 2

\((5x)^3+9^3=0\)
\((5x)^3=-9^3\)
\(5x=-9\)
\(x=-9/5\)

Answer 3

\[(5x^3)+7^3=(5x+7)((5x)^2-5x\times 7 + 7^2)\]

Answer 4

oh I forgot the imaginary ...

Answer 5

and cube root of 343 is 7 not 9 i think

Answer 6

yes :) you were right sattelite. So ignore my answer :D.

Answer 7

i am using \[a^3+b^3=(a+b)(a^2-ab+b^2)\]

Answer 8

-7/5
7^3 = 343

Answer 9

we need two more complex solutions dumbcow

Answer 10

so we have \[(5x+7)(25x^2-35x+49)=0\]
\[5x+7=0\]
\[x=-\frac{7}{5}\]

Answer 11

and the other two you find using the quadratic formula.

Answer 12

i will write them out if you like

Answer 13

\[\frac{35\pm \sqrt{35^2-4\times 25\times 49}}{2\times 25}\]
\[\frac{35\pm \sqrt{-3675}}{50}\]
\[\frac{35\pm 5\sqrt{147}i}{50}\]
\[\frac{7\pm \sqrt{147}i}{10}\]