Multiple choice

The nature of the roots of the equation $x^2 - 5x + 7 = 0$ is

  1. No real roots

  2. 1 real root and 1 imaginary

  3. Real and unequal

  4. Real and equal
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The discriminant D = b^2 - 4ac = (-5)^2 - 4(1)(7) = 25 - 28 = -3. Since D < 0, the roots are not real.

AI explanation

To find the nature of the roots, we calculate the discriminant using the formula b squared minus 4ac for the equation x squared minus 5x plus 7 equals 0. Substituting the values gives negative 5 squared minus 4 times 1 times 7, which equals 25 minus 28. Since the discriminant is negative 3, which is less than zero, the equation has no real roots.

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