Quadratic Formula

Definition

The quadratic formula is a formula used to solve quadratic equations of the form:

ax^2 + bx + c = 0

The quadratic formula is:

Where:

• a, b, and c are the coefficients from the quadratic equation ax^2 + bx + c = 0.

• The symbol  means "plus or minus," indicating two possible solutions (one for addition and one for subtraction).

Steps for using the quadratic formula:

1. Identify the values of a, b, and c from the given quadratic equation.

2. Plug these values into the quadratic formula.

3. Simplify the expression under the square root (the discriminant), b^2 - 4ac.

4. Solve for x, which may give two real solutions, one real solution, or no real solutions (if the discriminant is negative).

Example:

For the equation 2x^2 + 3x - 5 = 0, the coefficients are:

• a = 2

• b = 3

• c = -5

Using the quadratic formula:

This gives two solutions:

1. x = (-3 + 7)/4 = 4/4 = 1

2. x = (-3 - 7)/4 = -10/4 = -2.5

So the solutions are x = 1 and x = -2.5.

The quadratic formula is a powerful tool for solving any quadratic equation, even if factoring is difficult or impossible.

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