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# 04 - Let's Recap - Quadratic equation - Class 10 - Maths Class 10 Notes | EduRev

## Crash Course for Class 10 Maths by Let's tute

Created by: Letstute

## Class 10 : 04 - Let's Recap - Quadratic equation - Class 10 - Maths Class 10 Notes | EduRev

``` Page 1

(Quadratic equation is an equation in which the highest power of an
unknown variable is 2)

Any equation of the form p(x) = 0, where p(x) is a polynomial of
degree/power 2, is a quadratic equation.

Example:

,

,

, etc.

2. Standard Form of Quadratic Equation:
When we write the terms of p(x) in descending order of their degrees,
then we get the standard form of the equation i.e.

,

where a, b, c are real numbers, a ? 0.

3. Methods to find roots/solutions of a quadratic
equation:

a. Factorization method
b. Completing the square method
c. Discriminant method
Page 2

(Quadratic equation is an equation in which the highest power of an
unknown variable is 2)

Any equation of the form p(x) = 0, where p(x) is a polynomial of
degree/power 2, is a quadratic equation.

Example:

,

,

, etc.

2. Standard Form of Quadratic Equation:
When we write the terms of p(x) in descending order of their degrees,
then we get the standard form of the equation i.e.

,

where a, b, c are real numbers, a ? 0.

3. Methods to find roots/solutions of a quadratic
equation:

a. Factorization method
b. Completing the square method
c. Discriminant method

4. Solution of a Quadratic Equation by Factorization:
a. A real number a is said to be a root of the quadratic equation

, if

we can say that x = a is a

Note:

b. If we factorize

, a ? 0, into a product of two linear
factors, then the roots of the quadratic equation

can be found by equating each factor to zero.
Example:

The roots of

are the values of x for which

(3x – 2)(2x + 1) = 0

(3x – 2) = 0           or     (2x + 1) = 0

polynomial ?? ??
???? ??
equation ?? ??
???? ??

Page 3

(Quadratic equation is an equation in which the highest power of an
unknown variable is 2)

Any equation of the form p(x) = 0, where p(x) is a polynomial of
degree/power 2, is a quadratic equation.

Example:

,

,

, etc.

2. Standard Form of Quadratic Equation:
When we write the terms of p(x) in descending order of their degrees,
then we get the standard form of the equation i.e.

,

where a, b, c are real numbers, a ? 0.

3. Methods to find roots/solutions of a quadratic
equation:

a. Factorization method
b. Completing the square method
c. Discriminant method

4. Solution of a Quadratic Equation by Factorization:
a. A real number a is said to be a root of the quadratic equation

, if

we can say that x = a is a

Note:

b. If we factorize

, a ? 0, into a product of two linear
factors, then the roots of the quadratic equation

can be found by equating each factor to zero.
Example:

The roots of

are the values of x for which

(3x – 2)(2x + 1) = 0

(3x – 2) = 0           or     (2x + 1) = 0

polynomial ?? ??
???? ??
equation ?? ??
???? ??

Note:
For equations with coefficient of ??
other than 1, divide the whole equation by
the same number on both the sides to get 1 as the coefficient of ??
and then start
the process of completing the square.

5. Solution of a Quadratic Equation by Completing The
Square:

Page 4

(Quadratic equation is an equation in which the highest power of an
unknown variable is 2)

Any equation of the form p(x) = 0, where p(x) is a polynomial of
degree/power 2, is a quadratic equation.

Example:

,

,

, etc.

2. Standard Form of Quadratic Equation:
When we write the terms of p(x) in descending order of their degrees,
then we get the standard form of the equation i.e.

,

where a, b, c are real numbers, a ? 0.

3. Methods to find roots/solutions of a quadratic
equation:

a. Factorization method
b. Completing the square method
c. Discriminant method

4. Solution of a Quadratic Equation by Factorization:
a. A real number a is said to be a root of the quadratic equation

, if

we can say that x = a is a

Note:

b. If we factorize

, a ? 0, into a product of two linear
factors, then the roots of the quadratic equation

can be found by equating each factor to zero.
Example:

The roots of

are the values of x for which

(3x – 2)(2x + 1) = 0

(3x – 2) = 0           or     (2x + 1) = 0

polynomial ?? ??
???? ??
equation ?? ??
???? ??

Note:
For equations with coefficient of ??
other than 1, divide the whole equation by
the same number on both the sides to get 1 as the coefficient of ??
and then start
the process of completing the square.

5. Solution of a Quadratic Equation by Completing The
Square:

6. Discriminant:
A discriminant of a quadratic equation determines whether the

has real roots or not.
Note: Check point no. 7: Nature of the roots

DISCRIMINANT =

The roots of a quadratic equation

are given by

v

Where, DISCRIMINANT     (Discriminant =

)

8. Nature of the roots:

has

a. Two distinct real roots, if

b. Two equal roots, if

c. No real roots, if

```
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## Crash Course for Class 10 Maths by Let's tute

88 videos|31 docs

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