NCERT Class 10 Mathematics Quadratic Equation CBSE Board Sample Problems (For CBSE, ICSE, IAS, NET, NRA 2022)

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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

How to Solve Quadratic Equation
S. noMethodWorking
1factorizationThis 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

2Square methodIn 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

3Quadratic methodFor 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

Nature of Roots of Quadratic Equation
S. noConditionNature of roots
1Two distinct real roots
2One real root
3No real roots

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