Quadratic Formula

vCalc Reviewed
Equation / Last modified by Administrator on 2015/12/24 07:08
`"Quadratic Solutions" = `
Quadratic Formula
Variable Instructions Datatype
a Enter the a coefficient Decimal
b Enter the b coefficient Decimal
c Enter the constant c Decimal
Rating
ID
vCalc.Quadratic Formula
UUID
7ffee913-39d5-11e3-bfbe-bc764e049c3d

This is the equation for the solution of a second order polynomial of the form `aX^2+bX+C = 0` where  the solution produces two roots

`(-b +- sqrt(b^2 -4ac))/(2a)`

Notes

Solving the quadratic equation.
 Suppose `a x^2+b x+c=0`       and  `a!=0`

first divide by `a`   to get:

        `x^2+b/a x+c/a=0`

Then complete the square and obtain:

        `x^2+b/a x+(b/(2a))^2-(b/(2a))^2+c/a=0`

The first three terms factor:

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

Take square roots on both sides to get

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

Finally move the b/(2a) to the right and simplify to get the two solutions:

   `x_(1,2)=(-b+-sqrt(b^2-4a c))/(2a)`