Welcome to our quadratic formula calculator, where you can easily calculate the roots of a quadratic equation. This quadratic formula solver can even find complex roots if they exist! In this article, we shall discuss how to solve quadratic equations using the quadratic formula, so stick around to learn more! Show Solving quadratic equationsA quadratic equation is a second-degree polynomial equation, meaning that the largest power of the variable xx must be 2. The standard form of this quadratic equation is: Ax 2+Bx+C=0Ax^2 + Bx + C = 0 where:
Quadratic equations describe parabolas. You can check out how they look on a graph using our polynomial graphing calculator. 🙋 We call the solutions to a polynomial equation its roots. A quadratic equation can have two roots. There are other nonstandard forms, which we must first rearrange and reduce to the standard form. This quadratic function calculator accepts two such forms. If you can reduce your equation to the standard quadratic equation form, you can easily calculate its roots using the quadratic formula: x=−B±B2−4AC2Ax = \frac{-B \pm \sqrt{B^2 - 4AC}}{2A} For example, lets calculate the roots of the quadratic equation 2x2+4x−6=02x^2 + 4x - 6 = 0:
x1=−4+82×2=1\qquad x_1 = \frac{-4 + 8}{2\times2} = 1
x2=−4−82×2=−3\qquad x_2 = \frac{-4-8}{2\times2} = -3
Real and complex rootsDue to the nature of a square root, the square root term in the quadratic formula is crucial in determining whether the quadratic equation will have real roots or complex roots. Aptly, we call it the discriminant term (NOT to be confused with determinant!).
For example, let's calculate the roots of the quadratic equation 2x2+4x+6=02x^2 + 4x + 6 = 0.
x1=−4+−324 =−4+−324=−4 +i16×24=−4+4i24x 1=−1+i2\qquad\begin{align*} x_1 &= \frac{-4 + \sqrt{-32} }{4}\\ &= \frac{-4 + \sqrt{-32} }{4}\\ &= \frac{-4 + i\sqrt{16\times2} }{4}\\ &=\frac{-4 + 4i\sqrt{2} }{4}\\ x_1 &= -1 + i\sqrt{2} \end{align*}
How to use this quadratic formula calculatorThis quadratic formula calculator will not only calculate the roots of the quadratic equation but can also show you the steps involved! Here is how you unlock the awesomeness of our quadratic formula solver:
How many solutions does a complex quadratic equation have?A quadratic equation with real or complex coefficients has two solutions, called roots. These two solutions may or may not be distinct, and they may or may not be real.
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