Step-by-step explanation:
x^3-8 = 0
or, x^3 = 8
or, x = 8×(1/3)
or, x = 2
All solutions to the equation are x = 2, -1 + i√3, and -1 - i√3 two roots are complex and one root is real.
It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
We have:
x³ - 8 = 0
Using identity:
a³ - b³ = (a - b)(a² + ab + b²)
(x - 2)(x² + 2x + 4) = 0
x = 2
x² + 2x + 4 = 0
Using quadratic formula:
[tex]\rm x = \dfrac{-2 \pm\sqrt{2^2-4(1)(4)}}{2(1)}[/tex]
x = -1 ± i√3
Thus, all solutions to the equation are x = 2, -1 + i√3, and -1 - i√3 two roots are complex and one root is real.
Learn more about the complex number here:
brainly.com/question/10251853
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