What is Quadratic equation solver

The quadratic equation solver is an online calculator to solve a standard quadratic equation.

As the name suggests, Quadratic equation solver solves any quadratic equation,
which is in the form of ax^{2} + bx + c = 0, where a ≠ 0, using a Quadratic Formula.

By solving the quadratic equation, Quadratic Equation Solver arrives at values of x, for which the quadratic equation ax^{2} + bx + c = 0
holds true. This means, that when we replace x in ax^{2} + bx + c with the values calculated from quadratic equation solver, then ax^{2} + bx + c
calculates to zero.

The simple formula to calculate the values of x for which ax^{2} + bx + c = 0 holds true, is called Quadratic Formula:

Roots(x_{1}, x_{2}) = | −b ± √ b2 − 4ac |

2a |

As you can notice in the formula. This implies, Quadratic formula calculates two values of x: x_{1} and x_{2}, where

x_{1} = | −b + √ b2 − 4ac |

2a |

x_{2} = | −b - √ b2 − 4ac |

2a |

These two values of x for which ax^{2} + bx + c = 0 holds true, are called solutions of Quadratic Equation, also called roots of Quadratic Equation.

Nature of roots of Quadratic Equation

◾ If b^{2} – 4ac > 0, then √b2 − 4ac is real; hence we get two real and distinct roots.

◾ If b^{2} – 4ac = 0, then √b2 − 4ac is also zero; hence values of both x_{1} and x_{2} would be same and hence we get real and equal roots.

◾ If b^{2} – 4ac < 0, then √b2 − 4ac is imaginary number; hence we get imaginary roots.

◾ If b^{2} – 4ac is a perfect square, then √b2 − 4ac is a rational number; hence we get rational roots, else we get irrational roots.

How to use Quadratic equation solver

**Step 1** - Convert the Quadratic Equation you wish to solve in Standard Form of Quadratic Equation, ax^{2} + bx + c = 0

For example, if you have a quadratic equation in the form of x^{2} - 6x = -8, then convert it into Standard Form of Quadratic Equation.

x^{2} -6x = -8 is converted into x^{2} - 6x + 8 = 0

**Step 2** - Find value of coefficient a, b and c by comparing it with Standard Form of Quadratic Equation ax^{2} + bx + c = 0

For example, comparing x^{2} - 6x - 8 = 0 with ax^{2} + bx + c = 0, we get

a = 1,

b = -6,

c = 8

**Step 3**

Roots(x_{1}, x_{2}) = | −b ± √ b2 − 4ac |

2a |

x_{1} = | −b + √ b2 − 4ac |

2a |

= | −(-6) + √ (-6)2 − 4(1)(8) | = 4 |

2(1) |

x_{2} = | −b - √ b2 − 4ac |

2a |

= | −(-6) - √ (-6)2 − 4(1)(8) | = 2 |

2(1) |

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