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"Evaluate the discriminant for the equation. Determine the number of real solutions.

5x² + 2x + 6 = 0
What is the discriminant of the quadratic equation?

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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.

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