**One Zero of a Quadratic Equation**

A quadratic equation is a polynomial equation of degree 2, which can be written in the form P(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0. The zeros or roots of a quadratic equation are the values of x that make the equation equal to zero. In other words, they are the values of x for which P(x) = 0.

If P(x) = ax² + bx + c, then we can solve for the zeros of the equation by setting P(x) equal to zero and solving for x. Let's consider the quadratic equation P(x) = 0 in more detail.

**Quadratic Equation: P(x) = ax² + bx + c**

The general form of a quadratic equation is given by P(x) = ax² + bx + c, where a, b, and c are constants.

**Setting P(x) = 0 and Solving for x**

To find the zeros of the quadratic equation, we set P(x) equal to zero and solve for x.

P(x) = ax² + bx + c = 0

**Applying the Quadratic Formula**

The quadratic formula is a useful tool for solving quadratic equations. It states that for any quadratic equation of the form ax² + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± √(b² - 4ac)) / (2a)

**Finding the Zeros of the Quadratic Equation**

Using the quadratic formula, we can find the zeros of the quadratic equation P(x) = ax² + bx + c.

x = (-b ± √(b² - 4ac)) / (2a)

For P(x) = ax² + bx + c, the zeros of the equation are the values of x that make P(x) equal to zero.

Hence, the zero(s) of the quadratic equation can be found by substituting the values of a, b, and c into the quadratic formula and solving for x. The discriminant (b² - 4ac) determines the nature of the zeros:
- If the discriminant is positive, there are two distinct real zeros.
- If the discriminant is zero, there is one real zero (also known as a repeated or double zero).
- If the discriminant is negative, there are two complex conjugate zeros.

By following the steps mentioned above, you can find the zero(s) of a quadratic equation and determine its nature based on the discriminant. Remember to apply the quadratic formula correctly and simplify the expression to obtain the final solutions for x.