Manuals/calci/QUADRATIC

QUADRATIC(a,b,c)

• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} ,Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c} are any real numbers.

Description

• This function gives the root values of a quadratic equation.
• In elemetary algebra, general quadratic equation is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a{x^2}+bx+c} where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} ,Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c} are constant values and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} is unknown.
• Constant Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} cannot be equal to zero(0).
• The roots of a quadratic equation can be calculated as -

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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