We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
145
1
avatar

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

 May 13, 2019
 #1
avatar+28236 
+4

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

11 Online Users