How to Use the Quadratic Formula to Solve Equations: A Comprehensive Guide for Beginners

Quadratic Formula

The quadratic formula is a formula used to solve quadratic equations of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable

The quadratic formula is a formula used to solve quadratic equations of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.

The quadratic formula is given by:

x = (-b ± √(b^2 – 4ac)) / (2a)

Let’s break down the formula:

– The ± symbol indicates that there are two possible solutions, one with a positive sign and the other with a negative sign.
– The expression inside the square root (b^2 – 4ac) is called the discriminant. The value of the discriminant determines the nature of the solutions:
– If the discriminant is positive (b^2 – 4ac > 0), then there are two distinct real solutions.
– If the discriminant is zero (b^2 – 4ac = 0), then there is one real solution called a “root of multiplicity 2”, where both roots are the same.
– If the discriminant is negative (b^2 – 4ac < 0), then there are no real solutions. The solutions are complex numbers. To use the quadratic formula, follow these steps: 1. Determine the values of a, b, and c from the given quadratic equation. 2. Substitute the values of a, b, and c into the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a) 3. Simplify the expression inside the square root and calculate the discriminant (b^2 - 4ac). 4. Based on the value of the discriminant, determine the nature of the solutions. 5. If the discriminant is positive, evaluate both solutions using the plus (+) and minus (-) signs before the square root. 6. If the discriminant is zero, evaluate the single solution. 7. If the discriminant is negative, understand that there are no real solutions, only complex solutions. Remember to always simplify your answers as much as possible and provide both the exact and approximate values, if necessary. I hope this explanation helps you understand the quadratic formula better and guides you on how to use it to solve quadratic equations.

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