vCalc Reviewed
"Quadratic Solutions" =
Variable Instructions Datatype
a Enter the a coefficient Decimal
b Enter the b coefficient Decimal
c Enter the constant c Decimal
Type
Equation
Category
Mathematics->Algebra
Contents
3 variables
Tags:
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

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)