Exploring the Quadratic Formula | How to Find the Roots of a Quadratic Equation

Quadratic Formula

The quadratic formula is a mathematical formula used to find the solutions (or roots) of a quadratic equation

The quadratic formula is a mathematical formula used to find the solutions (or roots) of a quadratic equation. A quadratic equation is an equation in the form of ax^2 + bx + c = 0, where a, b, and c are constants. The quadratic formula states that the roots of this equation can be found using the following formula:

x = (-b ± √(b^2 – 4ac)) / 2a

In this formula:
– “x” represents the variable or unknown value being solved for.
– “-b” represents the opposite of the coefficient of the linear term (bx).
– “±” indicates that there are two possible solutions: one with a plus sign and one with a minus sign.
– “√” (square root) represents the mathematical operation of finding the non-negative square root.
– “b^2 – 4ac” is the discriminant, which measures the nature of the roots. If the discriminant is positive, the equation has two distinct real roots. If it is zero, the equation has one real root (also called a repeated root). And if it is negative, the equation has two complex roots (conjugate pairs).

To use the quadratic formula, you need to know the values of the coefficients a, b, and c in your quadratic equation. Simply substitute these values into the formula, perform the necessary calculations, and you will obtain the solutions for x.

It is important to note that if the discriminant is negative, the solutions will involve imaginary numbers or complex numbers. In such cases, the solutions will be in the form of a + bi, where “a” and “b” are real numbers and “i” represents the imaginary unit (√(-1)).

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