Final answer:
The discriminant is a part of the quadratic formula that helps determine the number of real solutions of a quadratic equation. In the equation 5x² + 2x + 6 = 0, the discriminant is -116, indicating that the equation has no real solutions.
Step-by-step explanation:
The discriminant is a part of the quadratic formula that helps determine the number of real solutions of a quadratic equation. The discriminant can be found by using the formula: Discriminant = b^2 - 4ac. In the equation 5x² + 2x + 6 = 0, the coefficients a, b, and c are 5, 2, and 6 respectively. Substituting these values, we have: Discriminant = (2)^2 - 4(5)(6) = 4 - 120 = -116.
Since the discriminant is negative (-116), it means that the quadratic equation has no real solutions. It only has two complex solutions.