The equation x^4 + x^2 + 1 = 0 has no real solutions

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Prove or disprove the following statement, if true write a formal proof.

The equation x^4 + x^2 + 1 = 0 has no real solutions. 

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Step 1: we prove this statement true or false.

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Why did you use discriminate and how exactly does it work for this proof?

Is there another way to prove it false aside from using discriminat, if so how? 

 

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Prove or disprove the following statement, if true write a formal proof.

The equation x^4 + x^2 + 1 = 0 has no real solutions. 

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