Question

Evaluate the discriminant for the following equation. Then use it to determine the number of distinct solutions, and tell whether they are rational, irrational, or nonreal complex numbers. 2x = -2x + 1

Answer 1

The discriminant is -4.

the equation 2x = -2x + 1 has two nonreal complex solutions.

Explanation:

To evaluate the discriminant of the equation 2x = -2x + 1, we first need to rearrange the equation into standard form, which is ax^2 + bx + c = 0. In this case, our equation is already in standard form.

The discriminant (D) of a quadratic equation is given by the formula D = b^2 - 4ac. Here, a = 2, b = -2, and c = 1. Plugging these values into the formula, we have:

D = (-2)^2 - 4(2)(1)

D = 4 - 8

D = -4

The discriminant is -4.

The discriminant helps us determine the number and type of solutions.

1. If the discriminant (D) is positive, then the quadratic equation has two distinct real solutions.

2. If the discriminant (D) is zero, then the quadratic equation has one real solution (a repeated root).

3. If the discriminant (D) is negative, then the quadratic equation has two nonreal complex solutions.

In this case, since the discriminant is -4 (negative), the equation 2x = -2x + 1 has two nonreal complex solutions.