Quadratic formula

There are many cases where the resolution of a quadratic equation by factoring or completing the square is not easy because it requires a lot of handling. In these cases, quadratic formula is quite useful and time saving way to solve the quadratic equations.

As we know a quadratic equation is an equation of the form ax^{2} + bx + c = 0 where a, b, and c are constants and a ≠ 0

For any such quadratic equation, the quadratic formula is:

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

2a |

Step by step process to solve the quadratic equation by quadratic formula:

**Step I: ** Arrange the Quadratic Equation in the standard form of ax^{2} + bx + c = 0.

**Step II: ** Compare the quadratic equation which is to be solved with the standard form of quadratic equation and find out the values of the coefficients a, b, and c.

**Step III: ** Put these values of a, b, and c in 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, or roots of Quadratic Equation.**

**Example:** Solve, x^{2} - 10x = -24

**Step I:** - Convert above equation in standard form of quadratic equation, ax^{2} + bx + c = 0

x^{2} -12x = -32 is converted into x^{2} - 12x + 32 = 0

**Step II:** - Now find the value of coefficients a, b and c by comparing it with standard form of quadratic equation ax^{2} + bx + c = 0

Comparing x^{2} - 12x + 32 = 0 with ax^{2} + bx + c = 0, we get

a = 1,

b = -12,

c = 32

**Step III:** Putting values of a, b and c in the quadratic formula

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

2a |

x_{1} = |
−b + √ b2 − 4ac |

2a |

= | −(-12) + √ (-12)2 − 4(1)(32) | = 8 |

2(1) |

x_{2} = |
−b - √ b2 − 4ac |

2a |

= | −(-12) - √ (-12)2 − 4(1)(32) | = 4 |

2(1) |

8 and 4 are the roots of the quadratic equation x^{2} -12x = -32

© 2020-2030 Amibba Systems Private Limited. All rights reserved.