Question

Use the discriminant to determine the number and nature of the solutions to x^2 + 2x + 1 = 0. Please show work.

Answer 1

The discriminant is used to determine the number and nature of solutions to a quadratic equation. In this case, the discriminant is equal to 0, indicating a double root.

Step-by-step explanation:

To determine the number and nature of solutions to the quadratic equation x² + 2x + 1 = 0, we can use the discriminant. The discriminant is the expression inside the square root in the quadratic formula.

For the equation ax² + bx + c = 0, the discriminant is given by b² - 4ac.

In this case, a = 1, b = 2, and c = 1. Substituting these values, we have:

Discriminant = 2² - 4(1)(1) = 4 - 4 = 0.

Since the discriminant is equal to 0, there is only one solution to the equation. This solution is called a double root.