# Manuals/calci/QUADRATIC

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**QUADRATIC(a,b,c)**

- , and are any real numbers.
- QUADRATIC(),returns the quadratic equation

## Description

- This function gives the root values of a quadratic equation.
- In elementary algebra, general quadratic equation is where , and are constant values and is unknown.
- Constant cannot be equal to zero(0).
- The roots of a quadratic equation can be calculated as -

and

- Geometrically, these roots represent the x values at which any parabola, explicitly given as y = ax2 + bx + c, crosses the x-axis.
- The name Quadratic comes from "quad" meaning square, because the variable gets squared (like x^2).

It is also called an "Equation of Degree 2" (because of the "2" on the x)

- Discriminant:

**(b^2 − 4ac)** in the formula above is called the Discriminant, because it can "discriminate" between the possible types of answer:

when (b^2 − 4ac) is positive, we get two Real solutions

when it is zero, we get just ONE real solution (both answers are the same)

when it is negative, we get two Complex solutions.

## Examples

- =QUADRATIC(5,6,1)=-1 ; -0.2
- =QUADRATIC(5,2,1)=-0.2-ⅈ0.4 ; -0.2+ⅈ0.4
- =QUADRATIC(2,3,4)= -0.75-ⅈ1.1989578808281798 ; -0.75+ⅈ1.1989578808281798

## Related Videos

## See Also

## References