Answer
No.
Work Step by Step
In this case, irrational solutions always come in conjugate pairs, thus
it is not possible for the solution set of a quadratic equation with integer coefficients to consist of a single irrational number.
Precalculus (6th Edition)
by Lial, Margaret L.; Hornsby, John; Schneider, David I.; Daniels, Callie
Published by
Pearson
ISBN 10:
013421742X
ISBN 13:
978-0-13421-742-0
Chapter 1 - Equations and Inequalities - 1.4 Quadratic Equations - 1.4 Exercises - Page 123: 93
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