NCERT Class 10 Mathematics Formula CBSE Board Sample Problems Part 5

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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

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

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Condition

Nature of roots

1

Two distinct real roots

2

One real root

3

No real roots