# NCERT Class 10 Mathematics Formula CBSE Board Sample Problems Part 5 (For CBSE, ICSE, IAS, NET, NRA 2022)

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## Quadratic Equations

S. no | Term | Descriptions |

1 | Quadratic Polynomial | P (x) where |

2 | Quadratic equation | where |

3 | Solution or root of the Quadratic equation | A real number a is called the root or solution of the quadratic equation if |

4 | Zeroes of the polynomial p (x) . | The root of the quadratic equation are called zeroes |

5 | Maximum roots of quadratic equations | We know from chapter two that a polynomial of degree can have max two zeroes. So a quadratic equation can have maximum two roots |

6 | Condition for real roots | A quadratic equation has real roots if |

### How to Solve Quadratic Equation

S. no | Method | Working |

1 | factorization | This method we factorize the equation by splitting the middle term b In Example (1) First we need to multiple the coefficient a and c. ln this case (2) Splitting the middle term so that multiplication is 12 and difference is the coefficient b (3) Roots of the equation can be find equating the factors to zero |

2 | Square method | In this method, we create square on LHS and RHS and then find the value. (1) (2) (3) (4) Example (1) (2) (3) Roots of the equation can be find using square root on both the sides |

3 | Quadratic method | For quadratic equation roots are given by For , Quadratic equation has two real roots of different value For quadratic equation has one real root For , no real roots for quadratic equation |

### Nature of Roots of Quadratic Equation

S. no | Condition | Nature of roots |

1 | Two distinct real roots | |

2 | One real root | |

3 | No real roots |