How to Find the Zeros of a Quadratic Polynomial in 2023

What is a Quadratic Polynomial?

Put simply, a quadratic polynomial is a polynomial with two terms. It has the general form of ax² + bx + c, where a, b, and c are coefficients, and x is a variable. Quadratic polynomials can be used to model a variety of real-world phenomena, such as the height of a ball thrown in the air, or the amount of money you can save in a year.

What are Zeros?

The zeros of a quadratic polynomial are the values of x that make the polynomial equal to zero. These values can be found by solving a quadratic equation, which involves setting the polynomial equal to zero and then finding the values of x that make the equation true.

The Quadratic Formula

The most common way to find the zeros of a polynomial is to use the quadratic formula. The quadratic formula is an equation that can be used to find the zeros of any quadratic polynomial. It is written as: x = -b ± √b² – 4ac / 2a, where a, b, and c are the coefficients of the polynomial.

Using the Quadratic Formula to Find the Zeros

To use the quadratic formula to find the zeros of a polynomial, you must first identify the coefficients a, b, and c. Once these have been identified, the formula can be used to find the zeros. To do this, simply substitute the coefficients for the corresponding variables in the formula, and then solve for x. The result will be the value or values of x that make the polynomial equal to zero.

Conclusion

Finding the zeros of a quadratic polynomial can be a difficult task, but the quadratic formula makes it much simpler. By simply identifying the coefficients of the polynomial and then substituting them into the formula, you can quickly and easily find the zeros of the polynomial.