Introduction:
Finding the zeros of a quadratic equation is an important aspect of solving polynomial equations. The zeros of a quadratic equation are also called roots or solutions of the equation. In this guide, we will learn how to find the zeros of a quadratic equation with an example.

Steps to Find Zeros:
To find the zeros of a quadratic equation, we can follow the following steps:

1. Write the quadratic equation in standard form: ax^2 + bx + c = 0, where a, b, and c are constants.
2. Identify the values of a, b, and c from the equation.
3. Use the quadratic formula to find the roots of the equation. The quadratic formula is given as:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

4. Substitute the values of a, b, and c in the quadratic formula and simplify to find the roots.

Example:
Let's find the zeros of the quadratic equation: 3x^2 - x - 4.

1. The given equation is in the standard form: ax^2 + bx + c = 0, where a = 3, b = -1, and c = -4.
2. Identify the values of a, b, and c.
3. Use the quadratic formula to find the roots of the equation:

x = (-(-1) ± sqrt((-1)^2 - 4(3)(-4))) / 2(3)
x = (1 ± sqrt(1 + 48)) / 6
x = (1 ± sqrt(49)) / 6

4. Simplify the roots:

x1 = (1 + 7) / 6 = 4/3
x2 = (1 - 7) / 6 = -2/3

Therefore, the zeros of the quadratic equation 3x^2 - x - 4 are x = 4/3 and x = -2/3.

Conclusion:
Finding the zeros of a quadratic equation is an important skill in solving polynomial equations. By following the steps outlined in this guide, we can easily find the roots of any quadratic equation.