An algebra problem by Rakibul Hasan Emon

Algebra Level pending

If x 3 − 8 = 0 x^{3} - 8 = 0 , then how many roots (real and non-real) does the equation have?


The answer is 3.

Rakibul Hasan Emon by Rakibul Hasan Emon , 20, Bangladesh

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1 solution

Tommy Li
Feb 11, 2017

x 3 − 8 = 0 x^3-8 = 0

( x − 2 ) ( x 2 + 2 x + 4 ) = 0 (x-2)(x^2+2x+4) = 0

x = − 2 x = -2 or x = − 1 + 3 i x = -1+\sqrt{3}i or x = − 1 − 3 i x = -1-\sqrt{3}i

⇒ \Rightarrow 3 roots

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