## quadratic formula

### The quadratic formula is an algebraic formula used to solve quadratic equations

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

The quadratic formula is derived from completing the square. To find the values of x that satisfy the equation, we can use the quadratic formula:

x = (-b ± √(b^2 – 4ac)) / (2a)

In the formula, ± represents the two possible solutions of x, √ represents the square root operation, and b^2 – 4ac is called the discriminant. The discriminant determines the nature of the solutions:

1. If the discriminant is positive (b^2 – 4ac > 0), the equation has two distinct real solutions.

2. If the discriminant is zero (b^2 – 4ac = 0), the equation has one real solution (also known as a repeated or double root).

3. If the discriminant is negative (b^2 – 4ac < 0), the equation has no real solutions, but it has two complex solutions (conjugate pairs) involving the imaginary unit "i," such as x = (5 + 3i) and x = (5 - 3i).
To solve a quadratic equation using the quadratic formula, simply substitute the values of a, b, and c into the formula and calculate the solutions for x.

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