The roots of the quadratic equation x² + x – 1 = 0 are

Option: A) Irrational and distinct B) not real C ) rational and distinct D) real and equal

Answer: A) Irrational and distinct

Solution:

1. Identify the coefficients:
   
   • a = 1 (coefficient of x²)
   • b = 1 (coefficient of x)
   • c = -1 (constant term)
2. Apply the quadratic formula:

The quadratic formula is:

Substitute the values of a, b, and c:

x = (-1 ± √(1² – 4 * 1 * -1)) / 2 * 1

x = (-1 ± √(1 + 4)) / 2

x = (-1 ± √5) / 2

3. Determine the nature of the roots:
   
   • The discriminant (b² – 4ac) is 5, which is positive and not a perfect square.
   • Therefore, the roots are irrational and distinct.

Hence Answer: A) Irrational and distinct

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