Multiple choice

Determine the nature of the roots of the following equations from their discriminants. $y^2\,+\,8y\,+\,4\,=\,0$

  1. real and equal

  2. real and unequal

  3. Complex

  4. Cannot be determined
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B Correct answer
Explanation

The discriminant of the quadratic equation y^2 + 8y + 4 = 0 is D = b^2 - 4ac. Here, D = 8^2 - 4(1)(4) = 64 - 16 = 48. Since the discriminant is positive and not a perfect square, the roots are real, irrational, and unequal.

AI explanation

To determine the nature of the roots for y^2 + 8y + 4 = 0, calculate the discriminant using the formula D = b^2 - 4ac. Here, a = 1, b = 8, and c = 4, so D = (8)^2 - 4(1)(4) = 64 - 16, giving D = 48. Since the discriminant is greater than zero, the quadratic equation has real and unequal roots.

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