Solves for the x, the unknown variable, in the polynomial expression of degree 2, ax^{2}+bx+c=0. The solution is also known as the root or roots.

Note, the quadratic equation can also be solved by completing the square or factoring. However, these methods do not always provide an answer. The quadratic formula provides a solution to all quadratic equations.

The value and sign of the discriminant determines the solution type. Note, the discriminant is the expression under the square root sign.

Value of Discriminant | Type |

Negative (less than zero) | Two distinct complex or imaginary solutions or roots |

Equal to zero | Single real solution. This is also known as a double root solution. |

Positive (greater than zero) | Two distinct real solutions |

a | |

b | |

c |

Two solutions | ||

x_{1} |
= | 0.20416847668728 |

x_{2} |
= | 9.7958315233127 |

Coefficient or Constant | Description |

a | Quadratic. If a equals zero then the equation becomes a linear equation. |

b | Linear |

c | Constant |

Note on the graph and plot |

If the discriminant is negative, a line chart is not drawn. |

If the discriminant is equal to zero, the line will cross the x axis once. |

If the discriminant is positive, the line will cross the x axis twice. |

If the solution is not imaginary, then the y axis will be crossed once. |

Sobel, Max A., Lerner, Nobert. 1991. Precalculus Mathematics. Prentice Hall. 4th Edition.

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