``` 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

```

Mathematics (Maths) Class 10

126 videos|477 docs|105 tests

FAQs on Let's Recap: Quadratic Equation - Mathematics (Maths) Class 10

 1. What is a quadratic equation?
Ans. A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.
 2. How do you solve a quadratic equation by factorization?
Ans. To solve a quadratic equation by factorization, we need to factorize the equation and equate each factor to zero. By setting each factor equal to zero, we can find the values of x that satisfy the equation.
 3. Can all quadratic equations be solved by factorization?
Ans. No, not all quadratic equations can be solved by factorization. Some quadratic equations may have complex roots or may not be factorizable. In such cases, we need to use other methods like the quadratic formula or completing the square to solve the equation.
 4. What is the quadratic formula?
Ans. The quadratic formula is a formula used to solve quadratic equations of the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0. The formula is given by x = (-b ± √(b^2 - 4ac)) / (2a).
 5. How do you find the nature of the roots of a quadratic equation?
Ans. To find the nature of the roots of a quadratic equation, we can look at the discriminant (D) of the equation. If D > 0, the equation has two distinct real roots. If D = 0, the equation has two equal real roots. And if D < 0, the equation has two complex roots.

Mathematics (Maths) Class 10

126 videos|477 docs|105 tests

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