anonymous 5 years ago what are the real or imaginary solutions of the polynomial equation 125x^3 + 343 = 0

1. anonymous

factor the sum of two cubes.

2. watchmath

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

3. anonymous

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

4. watchmath

oh I forgot the imaginary ...

5. anonymous

and cube root of 343 is 7 not 9 i think

6. watchmath

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

7. anonymous

i am using $a^3+b^3=(a+b)(a^2-ab+b^2)$

8. dumbcow

-7/5 7^3 = 343

9. watchmath

we need two more complex solutions dumbcow

10. anonymous

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

11. anonymous

and the other two you find using the quadratic formula.

12. anonymous

i will write them out if you like

13. anonymous

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