How many solutions does 2x² − √5 x + 1 = 0 have?

Correct answer: No solution. The discriminant is D = (−√5)² − 4(2)(1) = 5 − 8 = −3, which is negative, so there is no real solution.

Background: A quadratic has no real roots if D < 0.

• One: One solution needs D = 0.
• Two distinct solutions: Two distinct solutions need D > 0.
• Infinite: An infinite number of solutions does not apply to a quadratic.

Did you know? The equation has two complex roots.

Memory trick: D < 0 → no real roots.