What is Quadratic Equation Calculator

The quadratic equation calculator is an extremely useful online calculator, which solves any given quadratic equation by using quadratic formula

We know, that for a quadratic equation ax^{2} + bx + c = 0, where a ≠ 0, the quadratic formula is:

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

2a |

After inserting values of a, b and c and solving the quadratic equation using the quadratic formula explained above, 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 the quadratic formula, also known as roots of quadratic equation. **These two roots are the output of quadratic equation calculator**

**Hence, Quadratic Equation 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 equation calculator provides us a solution of two real and distinct roots.

◾ If b^{2} – 4ac = 0, then √b2 − 4ac is also zero; in this case Quadratic equation calculator provides us a solution of real and equal roots.

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

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

How to use Quadratic equation solver

**Step 1** - At the first step in using Quadratic Equation calculator , we have to rearrange the Quadratic Equation we have, into what is known as Standard Form of Quadratic Equation, which is represented as ax^{2} + bx + c = 0

So, Let's suppose we have to solve a quadratic equation which is currently in the form of

x^{2} -11x = -24

So we rearrange this equation, so that is represented in the standard form ax^{2} + bx + c = 0. Hence,

x^{2} - 11x = -24 is now equal to x^{2} - 11x + 24 = 0.

Now the quadratic equation has been successfully converted into standard form

**Step 2** - Now, to use our Quadratic Equation calculator, we have to input coefficient a, b and c in the calculator. So our next step is to find coefficient a, b and c. So we compare our derived equation above in standard form x^{2} - 11x + 24= 0 with ax^{2} + bx +c = 0.

Hence, we get

a = 1,

b = -11,

c = 24

**Step 3**

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

2a |

x_{1} = | −b + √ b2 − 4ac |

2a |

= | −(-11) + √ (-11)2 − 4(1)(24) | = 8 |

2(1) |

x_{2} = | −b - √ b2 − 4ac |

2a |

= | −(-11) - √ (-11)2 − 4(1)(24) | = 3 |

2(1) |

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