Why do I get different answer when I use the quadratic equation? In finding the zeros of a function. I used factoring and completing the squares and it gave me the same answer..

How am I going to defend that my answer using quadatic formula is also right ?

Then you did something wrong.

It's great that you have used multiple methods to find the zeros of a quadratic function. Different methods may sometimes yield different answers due to various factors such as computation errors or the complexity of the equation. However, the quadratic formula is a reliable and foolproof method to find the zeros of any quadratic equation.

To defend your answer using the quadratic formula, you can follow these steps:

1. Understand the quadratic formula: The quadratic formula states that for any quadratic equation of the form ax^2 + bx + c = 0, the solutions (or zeros) can be found using the formula: x = (-b ± √(b^2 - 4ac)) / (2a).

2. Revisit your calculation: Double-check that you have correctly substituted the values of a, b, and c into the formula. Ensure you have correctly calculated the discriminant (b^2 - 4ac) and the square root of the discriminant (√(b^2 - 4ac)).

3. Simplify your answer: After substituting the values into the formula, simplify the equation as much as possible. Simplify the numerator and denominator by canceling out common factors, if any.

4. Evaluate the solution: Calculate the value of both solutions, one with the plus sign (+) and the other with the minus sign (-) in front of the square root. Keep the precision of your calculations intact to avoid any rounding errors.

5. Compare your answer with other methods: Compare the solutions obtained using the quadratic formula with the results from factoring and completing the square methods. Ensure the values are consistent and match.

By following these steps, you can confidently defend your answer obtained using the quadratic formula. Remember, the quadratic formula is a trusted mathematical tool derived from fundamental principles, and when correctly applied, it should provide the correct solutions to quadratic equations.