Multiple choice

The quadratic equations $\displaystyle x^{2}-5x+3=0$ has

  1. no real roots

  2. two distinct real roots

  3. two equal real roots

  4. more than two real roots
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Discriminant D = b^2 - 4ac = (-5)^2 - 4(1)(3) = 25 - 12 = 13. Since D > 0, the equation has two distinct real roots.

AI explanation

To determine the nature of the roots, we evaluate the discriminant D = b^2 - 4ac using the values a = 1, b = -5, and c = 3. Calculating this gives D = (-5)^2 - 4(1)(3) = 25 - 12 = 13. Since the discriminant is a positive number, the quadratic equation has two distinct real roots.

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