Question

The roots of the quadratic equation * 2x²-2(sqr rt 2x)+1=0

Answer 1

Answer:

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Step-by-step explanation:

The given equation is

2x² - 2√3 x + 3 = 0

Comparing with the standard equation

ax² + b x + c = 0

the cofficients a, b, and constant term c are:

a = 2; b = - 2√3 and c = 3.

And the discriminant D (= b² — 4 ac) for our equation is

D = (-2√3 )² — 4.2. 3 = [ (- √12)² — 24] = 12 - 24 = —12. Since the discriminant is negative, the roots of the equation would be complex and conjugate of each other.

And the roots of the standard quadratic equation are:

x = [ — b ± √D ]/2a

In our case

√D = √(— 12) = 2√3 i

and the roots

x = (+ 2√3 ± √-12)/4 = ¼[(2 +√3) ± (2 +√3) i] = [(2√3)/4] [ 1 ± i ] = (√3/2)(1 ± i)