What is Quadratic formula calculator

The quadratic formula calculator is an online calculator to solve a standard quadratic equation using the Quadratic Formula, which is -

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

2a |

After solving the quadratic equation using a quadratic formula calculator, we get two values:

x_{1} = | −b + √ b2 − 4ac |

2a |

x_{2} = | −b - √ b2 − 4ac |

2a |

These two values of x, x_{1} and x_{2}, which are calculated from Quadratic Formula Calculator, are also known as roots of quadratic equation.

**Hence, Quadratic Formula Calculator calculates roots of a Quadratic equation**

Nature of roots of Quadratic Equation

◾ If b^{2} – 4ac > 0, then √b2 − 4ac is real; in this case, Quadratic formula calculator gives us two real and distinct roots.

◾ If b^{2} – 4ac = 0, then √b2 − 4ac is zero; in this case, Quadratic formula calculator gives us real and equal roots.

◾ If b^{2} – 4ac < 0, then √b2 − 4ac is imaginary number; in this case, Quadratic formula calculator gives us imaginary roots.

◾ If b^{2} – 4ac is a perfect square, then √b2 − 4ac is a rational number; in this case, Quadratic formula calculator gives us rational roots, else Quadratic formula calculator gives us irrational roots

How to use Quadratic formula calculator

**Step 1** - To use the Quadratic formula calculator, we have to convert the Quadratic Equation to be calculated into Standard Form of Quadratic Equation, ax^{2} + bx + c = 0

For example, let' suppose, we have to solve a quadratic equation which is in the form, x^{2} - 9x = -20. So in this case, we will convert the quadratic equation into Standard Form of Quadratic Equation, ax^{2} + bx +c = 0

Hence, x^{2} - 9x = -20 in standard form would be x^{2} - 9x + 20 = 0

**Step 2** - Now, we have to compare the derived quadratic equation in standard form which is x^{2} - 9x + 20 = 0 with Standard Form of Quadratic Equation, ax^{2} + bx +c = 0 and find the value of a, b and c.

For example, comparing x^{2} - 9x + 20 = 0 with ax^{2} + bx + c = 0, we get

a = 1,

b = -9,

c = 20

**Step 3** - Once we have derived the value of coefficients a, b and c, then all we need is to insert these values in the quadratic formula, which is

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

2a |

x_{1} = | −b + √ b2 − 4ac |

2a |

= | −(-9) + √ (-9)2 − 4(1)(20) | = 5 |

2(1) |

x_{2} = | −b - √ b2 − 4ac |

2a |

= | −(-9) - √ (-9)2 − 4(1)(20) | = 4 |

2(1) |

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