# NCERT Class 10 Mathematics Quadratic Equation CBSE Board Sample Problems

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Quadratic Equation

Quadratic Polynomial

P(x) where

Quadratic equation

where

**Solution or root of the Quadratic equation**

A real number a is called the root or solution of the quadratic equation if

**Some other points to remember**

The root of the quadratic equation is the zeroes of the polynomial p(x).

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

A quadratic equation has no 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 |