``` Page 1

Equations
Page 2

Equations
Factorization Method
Completing The Square
Method
An equation of the form ax
2
+ bx + c = 0, where a, b & c are real numbers & a = 0 is known as a Quadratic Equation
A Polynomial of degree 2 is known as a Quadratic Polynomial
Method
ax
2
+ bx + c = 0 ax
2
+ bx + c = 0 ax
2
+ bx + c = 0
Multiply a & c
a x c = h
Find two numbers
whose product is h and sum is b
These two numbers
can be a and b or any other (p, q)
Split the middle term
accordingly &  take out the
common factors
Finally we’ll get a
product of two linear equations &
hence we can get two values of x
i.e. roots of the equation
Divide the entire equation
by a
Take the constant c / a
on R. H. S.
(    x coecient of x)
2
on both the sides (L.H.S. & R.H.S.)
So L.H.S. can be written as
where b is the
coecient of x
Now take square root on
both the sides & then simplify the
linear equation to get roots of x
Step 1 :
Step 2 :
Step 3 :
Step 4 :
Step 5 :
Step 1 :
Step 2 :
Step 4 :
Step 3 :
Step 5 :
1
2
Simply take a, b & c
with their respective sign
Find
the two roots of the equation
or
Step 1 :
Step 2 :
Step 3 :
-b ±   b
2
- 4ac
x =
2a
-b +   b
2
- 4ac
x =
2a
-b -    b
2
- 4ac
x =
2a
)
2
(x +
b
2a
Page 3

Equations
Factorization Method
Completing The Square
Method
An equation of the form ax
2
+ bx + c = 0, where a, b & c are real numbers & a = 0 is known as a Quadratic Equation
A Polynomial of degree 2 is known as a Quadratic Polynomial
Method
ax
2
+ bx + c = 0 ax
2
+ bx + c = 0 ax
2
+ bx + c = 0
Multiply a & c
a x c = h
Find two numbers
whose product is h and sum is b
These two numbers
can be a and b or any other (p, q)
Split the middle term
accordingly &  take out the
common factors
Finally we’ll get a
product of two linear equations &
hence we can get two values of x
i.e. roots of the equation
Divide the entire equation
by a
Take the constant c / a
on R. H. S.
(    x coecient of x)
2
on both the sides (L.H.S. & R.H.S.)
So L.H.S. can be written as
where b is the
coecient of x
Now take square root on
both the sides & then simplify the
linear equation to get roots of x
Step 1 :
Step 2 :
Step 3 :
Step 4 :
Step 5 :
Step 1 :
Step 2 :
Step 4 :
Step 3 :
Step 5 :
1
2
Simply take a, b & c
with their respective sign
Find
the two roots of the equation
or
Step 1 :
Step 2 :
Step 3 :
-b ±   b
2
- 4ac
x =
2a
-b +   b
2
- 4ac
x =
2a
-b -    b
2
- 4ac
x =
2a
)
2
(x +
b
2a
Nature of Roots: D = b
2
- 4ac
D iscriminant is known for discriminating real and non-real roots as well as
to dene nature of roots.
Conditions:
When  D = 0, roots are real & equal
When  D > 0, roots are real & unequal
When  D < 0, roots are non-real & unequal

and Factorization method
Scan the QR Codes to watch our free videos
Quadratic formula is derived from completing the square
method
In word questions, try to nd words like product, area,
Pythagoras theorem, etc; where we will multiply two terms
In word problem, the solution thus obtained should always be
checked with conditions given in the question.
Speed =      , please remember this formula.
A variety of questions on quadratic equations are based on the
concept of speed.  Also do remember conversions like
1 hour = 60 minutes, 1 minute = 60 seconds.
?
To determine whether an equation is quadratic or not, expand
the given equation,  simplify it as much as possible and then check
the highest degree.
?
?
?
?
Distance
Time
```

## Mathematics (Maths) Class 10

116 videos|420 docs|77 tests

## FAQs on Points to Remember: Quadratic Equations - Mathematics (Maths) Class 10

 1. What is a quadratic equation?
Ans. A quadratic equation is a polynomial equation of degree 2, where the highest power of the variable is 2. It can be written in 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?
Ans. To solve a quadratic equation, you can use various methods such as factoring, completing the square, or using the quadratic formula. The most commonly used method is the quadratic formula, which states that for any quadratic equation ax^2 + bx + c = 0, the solutions can be found using the formula x = (-b ± √(b^2 - 4ac)) / (2a).
 3. Can a quadratic equation have more than two solutions?
Ans. No, a quadratic equation can have at most two solutions. This is because a quadratic equation represents a parabola, which can intersect the x-axis at most twice. If the discriminant (b^2 - 4ac) is positive, the equation has two distinct real solutions. If the discriminant is zero, the equation has one real solution (a double root). If the discriminant is negative, the equation has two complex solutions.
 4. How are quadratic equations used in real life?
Ans. Quadratic equations have various real-life applications. They are used in physics to model the motion of objects under the influence of gravity, such as projectiles or falling bodies. They are also used in engineering to design structures, optimize processes, and analyze circuits. In finance, quadratic equations are used to calculate interest rates, determine break-even points, or solve optimization problems.
 5. Can a quadratic equation have no solutions?
Ans. Yes, a quadratic equation can have no solutions. This occurs when the discriminant (b^2 - 4ac) is negative. In such cases, the quadratic equation does not intersect the x-axis, and therefore, does not have any real solutions. However, it is still possible to find complex solutions using imaginary numbers.

## Mathematics (Maths) Class 10

116 videos|420 docs|77 tests

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