Mastering the Quadratic Formula: A Step-by-Step Guide to Solving Quadratic Equations

Quadratic Formula

The quadratic formula is a very useful tool in solving quadratic equations, which are equations of the form:
ax^2 + bx + c = 0

The quadratic formula is:
x = (-b ± √(b^2 – 4ac)) / 2a

In this formula, “x” represents the variable we are solving for, “a”, “b”, and “c” are coefficients of the quadratic equation

The quadratic formula is a very useful tool in solving quadratic equations, which are equations of the form:
ax^2 + bx + c = 0

The quadratic formula is:
x = (-b ± √(b^2 – 4ac)) / 2a

In this formula, “x” represents the variable we are solving for, “a”, “b”, and “c” are coefficients of the quadratic equation.

Here’s a step-by-step breakdown of how to use the quadratic formula:

1. Identify the values of “a”, “b”, and “c” in the quadratic equation.

2. Substitute these identified values into the quadratic formula, keeping track of the signs.

3. Simplify the expression under the square root (the discriminant), which is represented by (b^2 – 4ac). This will determine the nature of the solutions.

– If the discriminant is positive (√(b^2 – 4ac) > 0), there are two distinct real solutions.
– If the discriminant is zero (√(b^2 – 4ac) = 0), there is one real solution (also known as a double root).
– If the discriminant is negative (√(b^2 – 4ac) < 0), there are two complex solutions. 4. Calculate the square root of the discriminant and evaluate the numerator (which involves adding or subtracting the square root to -b). Then divide the entire numerator by 2a. 5. If the discriminant is positive, you will have two real solutions. - For example, if your solutions are x1 and x2, the solutions will be x1 = (-b + √(b^2 - 4ac)) / 2a and x2 = (-b - √(b^2 - 4ac)) / 2a. 6. If the discriminant is zero, you will have one real solution, double root. - For example, if your solution is x, it will be x = (-b ± √(b^2 - 4ac)) / 2a. 7. If the discriminant is negative, you will have two complex solutions. - For example, if your solutions are x1 and x2, the solutions will be x1 = (-b + i√(-b^2 + 4ac)) / 2a and x2 = (-b - i√(-b^2 + 4ac)) / 2a. In this case, "i" represents the imaginary unit, which is defined as the square root of -1. It's important to use the quadratic formula when the quadratic equation cannot be easily factored. This formula provides an efficient method for finding solutions to quadratic equations in any form.

More Answers: