Quadratic Equation Root Calculator

A quadratic equation of one unknown is a polynomial equation that contains only one unknown variable and the highest degree of the unknown variable is quadratic. The general form of the equation is: ax²+bx+c=0 (a≠0), where ax² is a quadratic term, bx is a linear term, c is a constant term, and a and b are constants. a≠0 is an important condition, otherwise it cannot be guaranteed that the highest degree of the unknown variable in the equation is quadratic.

When Δ=b^2-4ac≥0, x=[-b±(b^2-4ac)^(1/2)]/2a

When Δ=b^2-4ac＜0, x={-b±[(4ac-b^2)^(1/2)]i}/2a(i is an imaginary unit)

The method of matching quadratic equations:

ax^2+bx+c=0(a,b,c are constants)

x^2+bx/a+c/a=0

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

x+b/2a=±(b^2-4ac)^(1/2)/2a

x=[-b±(b^2-4ac)^(1/2)]/2a