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 a second-degree polynomial equation, usually written in the form:
ax^2 + bx + c = 0
The quadratic formula provides the values of x that satisfy this equation. It is given by:
x = (-b ± √(b^2 – 4ac)) / (2a)
In this equation, a, b, and c are coefficients of the quadratic equation. By plugging these values into the quadratic formula, we can calculate the two possible solutions for x, which are often referred to as the roots.
The discriminant, defined as the expression under the square root (√(b^2 – 4ac)), plays a crucial role in determining the nature of the solutions. If the discriminant is positive, then there are two distinct real solutions. If the discriminant is zero, then there is a single real solution (or a repeated root). And if the discriminant is negative, then there are no real solutions, and the quadratic equation has complex roots.
The quadratic formula is a powerful tool in algebra and provides a systematic way to solve quadratic equations efficiently. It is widely used in various fields such as physics, engineering, economics, and computer science.
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