Question

What are the real and complex solutions of the polynomial equation?
27x^3+125=0

Answer 1

Step by step, please

Answer 2

Use the sum of cubes formula \((a+b)^{3} = (a+b)(a^{2} - ab + b^{2})\) The (a+b) set equal to 0 will give you the real solution. Use the quadratic formula on the \(a^{2} - ab+b^{2}\) part in order to find the 2 complex roots.

Answer 3

Correction, \((a+b)^{3}\) should be \((a^{3} + b^{3})\) , my apologies.

Answer 4

Use the idea that \(27x^{3} = a^{3}\) and that \(125 = b^{3}\) in the formula.

Answer 5

Thanks

Answer 6

You're welcome :)

Answer 7

when you solve this question remember about signs
\(\color{red}{SOAP}\)
\(\color{green}{:)}\)