Multiple choice

The quadratic equation ${ 2x }^{ 2 }-\sqrt { 5x } +1=0$ has

  1. two distinct real roots

  2. two equal real roots

  3. no real roots

  4. more than 2 real roots
Reveal answer Fill a bubble to check yourself
C Correct answer
AI explanation

To determine the nature of the roots, we evaluate the discriminant D = b^2 - 4ac for the quadratic equation 2x^2 - sqrt(5)x + 1 = 0. Substituting a = 2, b = -sqrt(5), and c = 1 gives D = (-sqrt(5))^2 - 4(2)(1) = 5 - 8 = -3. Since the discriminant is less than zero, the quadratic equation has no real roots.

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