What is Roots Calculator

Roots calculator is a tool to calculate roots of any given quadratic equation, where we input value of coefficient a, b and c into the roots calculator.

Roots of a quadratic equation is basically the values of x for which quadratic equation ax^{2} + bx + c = 0 holds true.

These values of x for which quadratic equation ax2 + bx +c = 0 holds true are called the roots of a quadratic equation.

To calculate the roots of a quadratic equation, we apply the quadratic formula is, which is:

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

2a |

When we insert the value of a, b and c and solve 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 called roots of quadratic equation.

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

Nature of roots of Quadratic Equation

◾ If b^{2} – 4ac > 0, then √b2 − 4ac is real; here roots calculator provides us an output of two real and distinct roots.

◾ If b^{2} – 4ac = 0, then √b2 − 4ac is zero; here roots calculator provides us an output of only one real and equal root.

◾ If b^{2} – 4ac < 0, then √b2 − 4ac is imaginary number; here roots calculator provides us an output of imaginary roots.

◾ If b^{2} – 4ac is a perfect square, then √b2 − 4ac is a rational number; here roots calculator provides us an output of rational roots, else roots calculator provides us a solution of irrational roots.

How to use Roots calculator

**Step 1** - Arrange the Quadratic Equation into Standard Form of Quadratic Equation, which is represented as ax^{2} + bx + c = 0

So, if we have to solve a quadratic equation

x^{2} - 7x = -12

First arrange this equation into the standard form ax^{2} + bx +c = 0. Hence,

x^{2} - 7x = -12 is now equal to x^{2} - 7x + 12= 0.

Now the quadratic equation has been successfully converted into standard form

**Step 2** - Now, to use our Roots calculator, let's enter coefficient a, b and c in the calculator. So to find coefficient a, b and c, we compare our equation x^{2} - 7x + 12= 0 with ax^{2} + bx +c = 0.

Hence, we get

a = 1,

b = -7,

c = 12

**Step 3** - Insert the values of a, b and c in Quadratic formula:

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

2a |

x_{1} = | −b + √ b2 − 4ac |

2a |

= | −(-7) + √ (-7)2 − 4(1)(12) | = 4 |

2(1) |

x_{2} = | −b - √ b2 − 4ac |

2a |

= | −(-7) - √ (-7)2 − 4(1)(12) | = 3 |

2(1) |

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