Question

find the root of w^3 - 1= 0
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Answer 1

Answer:

1,  -1/2+√3i/2, -1/2-√3i/2

Step-by-step explanation:

w³ - 1 = 0

As, x³ - y ³ = (x - y)(x²+xy+y²)

so, w³ - 1 = 0

⇒ (x - 1)(x²+x+1) = 0

One of the root is x = 1

other roots can be obtained from equation:

(x²+x+1) = 0

using Sri Dharacharya formula:

x = $\frac{-b +- \sqrt{b^{2} - 4*a*c } }{2*a}$

x = -1/2 + √-3/2 or -1/2+√3i/2

x = -1/2 - √-3/2 or -1/2-√3i/2