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

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Quadratic Equations

Quadratic Equations
S. noTermDescriptions
1Quadratic PolynomialP (x) where
2Quadratic equation where
3Solution or root of the Quadratic equationA real number a is called the root or solution of the quadratic equation if

4Zeroes of the polynomial p (x) .The root of the quadratic equation are called zeroes
5Maximum roots of quadratic equationsWe know from chapter two that a polynomial of degree can have max two zeroes. So a quadratic equation can have maximum two roots
6Condition for real rootsA quadratic equation has 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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