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Find the number of real roots to \(x^4 - 2x^2 - 7 = 0.\)

 May 13, 2019
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Let y = x2.   Then y2 - 2y - 7 = 0.

 

Use the standard quadratic formula to find that y = 2√2 + 1  and  y = 1 - 2√2

 

Since x = ±√y we must have positive y for real roots.  Only 2√2 + 1 is positive, hence there are just two real roots of the original equation.

 May 13, 2019

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