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The Solving Quadratics Through The Quadratic Formula Calculator will calculate:

- Calculate the root(s) of the quadratic equation ax
^{2}+ bx + c = 0 by using the quadratic formula.

**Solving Quadratics Through The Quadratic Formula Calculator Parameters:** The discriminant must not be negative.

First root of the quadratic equation, x_{1} = |

Second root of the quadratic equation, x_{2} = |

First root of the quadratic equation Formula and Calculations |
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x_{1} = -b - √b^{2} - 4ac/2ax _{1} = - √^{2} - 4 × × /2 × x _{1} = - √ - /x _{1} = - √/x _{1} = - /x _{1} = /x _{1} = |

Second root of the quadratic equation Formula and Calculations |

x_{2} = -b + √b^{2} - 4ac/2ax _{2} = + √^{2} - 4 × × /2 × x _{2} = + √ - /x _{2} = + √/x _{2} = + /x _{2} = /x _{2} = |

Solving Quadratics Through The Quadratic Formula Calculator Input Values |

Coefficient (a) = |

Coefficient (b) = |

Constant (c) = |

Please note that the formula for each calculation along with detailed calculations is shown further below this page. As you enter the specific factors of each solving quadratics through the quadratic formula calculation, the Solving Quadratics Through The Quadratic Formula Calculator will automatically calculate the results and update the formula elements with each element of the solving quadratics through the quadratic formula calculation. You can then email or print this solving quadratics through the quadratic formula calculation as required for later use.

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A quadratic equation is a second-order equation with one variable of the form

y = ax^{2} + bx + c = 0

where x is the variable, a and b are coefficients and c is a constant.

For example, the equation 5x^{2} - 7x + 2 = 0 is a quadratic equation, where a = 5, b = -7 and c = 2.

A quadratic equation may have one or two roots or it may not have any root. The number of roots depends on the sign of the discriminant Δ, which is a mathematical sentence obtained by the equation

∆ = b^{2} - 4ac

Thus,

When the discriminant is positive (Δ > 0) the quadratic equation has two distinct roots:

x_{1} = ** -b - √∆/2a** and x

The joint form of the above formulas is called the quadratic formula, i.e.

x_{1,2} = *-b ∓ √∆**/**2a*

When the discriminant is zero (Δ = 0), the quadratic equation has two equal roots (practically, it has a single root):

x_{1} = x_{2} = *-b**/**2a*

When the discriminant is negative (Δ < 0), the quadratic equation has no real roots because it is impossible to find the square root of a negative number.

The following Math tutorials are provided within the Equations section of our Free Math Tutorials. Each Equations tutorial includes detailed Equations formula and example of how to calculate and resolve specific Equations questions and problems. At the end of each Equations tutorial you will find Equations revision questions with a hidden answer that reveal when clicked. This allows you to learn about Equations and test your knowledge of Math by answering the revision questions on Equations.

- 9.1 - Variables, Coefficients and Constants. First Order Equations with One Variable
- 9.2 - Word Problems Involving Equations
- 9.3 - Identities
- 9.4 - Iterative Methods for Solving Equations
- 9.5 - Quadratic Equations
- 9.6 - The Quadratic Formula
- 9.7 - Systems of Linear Equations. Methods for Solving Them.
- 9.8 - Relationship between Equations in Linear Systems. Systems of Equations with One Linear and One Quadratic Equation