Manuals/calci/QUADRATIC

QUADRATIC(a,b,c)

• $a$,$b$ and $c$ 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 $a{x^{2}}+bx+c$ where $a$,$b$ and $c$ are constant values and $x$ is unknown.
• Constant $a$ cannot be equal to zero(0).
• The roots of a quadratic equation can be calculated as -

$x=(-b+{\sqrt {b^{2}-4ac}})/2a$ and $x=(-b-{\sqrt {b^{2}-4ac}})/2a$

• 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

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

Related Videos

QUADRATIC EQUATION

See Also

• SQRT
• SQRTPI
• POWER

References

• Quadratic Formula

• List of Main Z Functions

• Z3 home