Quadratic Equation

The Quadratic Equation calculator returns the real value roots of a second degree polynomial of the form aX²+bX+C = 0.

INSTRUCTIONS:  Enter the following:

• (a) Coefficient of X²
• (b) Coefficient of X
• (c) Constant

Quadratic Roots (x):  The calculator returns the real value roots.  These are the values of x where the graph of the equation crosses the x axis where y is equal to zero.

Related Calculators

• Second Degree Polynomial
• Tangent Line of Second Degree Polynomial
• Quadratic Equation

The Math / Science

The Quadratic Equation computes the two solutions of a second order polynomial of the form:

         aX²+bX+ c = 0

The solutions (values of x) for the above can be found using the quadratic equation:

`x = (-b +- sqrt(b^2 -4*a*c))/(2*a)`

where:

• x = two solutions (+ and -) to the equation (roots)
• a = coefficient of X²
• b = coefficient of X
• c = constant 

Note, the algorithm in this equation precludes imaginary root (those including the square root of negative numbers).  For a derivation of the quadratic formula, see the video: https://www.youtube.com/watch?v=Sidv3d1SEXs&feature=youtu.be