Multiple choice

Determine the nature of roots of the following equation from the discriminant: $y^{2}\, -\, 5y\, +\, 11\, =\, 0$

  1. Real and equal

  2. Real and unequal

  3. nonreal.

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The discriminant D = b^2 - 4ac = (-5)^2 - 4(1)(11) = 25 - 44 = -19. Since the discriminant is negative, the roots are non-real (complex).

AI explanation

The nature of the roots is determined by the discriminant, calculated as D equals b squared minus 4ac. For the equation y squared minus 5y plus 11 equals 0, the discriminant is (-5) squared minus 4 times 1 times 11, which equals 25 minus 44, or -19. Because the discriminant is less than zero, the roots are nonreal.

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