# Quadratic Equations Class 10 PPT

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``` Page 1

EQUATIONS
Page 2

EQUATIONS
DEFINITION
• In Mathematics Quadratic Equation is  equation of second
degree.
• A quadratic equation in the variable x is an equation of
the form ax² + bx + c = 0, where a, b, c are real
numbers, a ? 0
Page 3

EQUATIONS
DEFINITION
• In Mathematics Quadratic Equation is  equation of second
degree.
• A quadratic equation in the variable x is an equation of
the form ax² + bx + c = 0, where a, b, c are real
numbers, a ? 0
• A real number a is said to be a root of the quadratic
equation ax²  + bx + c = 0, if  a a² + b a + c = 0.
The zeroes of the quadratic polynomial ax² + bx + c
and the roots of the quadratic equation ax² + bx + c
= 0 are the same.
Page 4

EQUATIONS
DEFINITION
• In Mathematics Quadratic Equation is  equation of second
degree.
• A quadratic equation in the variable x is an equation of
the form ax² + bx + c = 0, where a, b, c are real
numbers, a ? 0
• A real number a is said to be a root of the quadratic
equation ax²  + bx + c = 0, if  a a² + b a + c = 0.
The zeroes of the quadratic polynomial ax² + bx + c
and the roots of the quadratic equation ax² + bx + c
= 0 are the same.
CHECK WHETHER THE FOLLOWING ARE
Example:
(x – 2)
2
+ 1 = 2x – 3
• LHS = (x – 2)² + 1 = x² – 4x + 4 + 1 = x²  – 4x + 5
• Therefore, (x – 2) ² + 1 = 2x – 3 can be rewritten as
• x²   – 4x + 5 =  2x – 3
• i.e., x²  – 6x + 8 = 0
• It is of the form ax² + bx + c = 0.
• Therefore, the given equation is a quadratic equation.
Page 5

EQUATIONS
DEFINITION
• In Mathematics Quadratic Equation is  equation of second
degree.
• A quadratic equation in the variable x is an equation of
the form ax² + bx + c = 0, where a, b, c are real
numbers, a ? 0
• A real number a is said to be a root of the quadratic
equation ax²  + bx + c = 0, if  a a² + b a + c = 0.
The zeroes of the quadratic polynomial ax² + bx + c
and the roots of the quadratic equation ax² + bx + c
= 0 are the same.
CHECK WHETHER THE FOLLOWING ARE
Example:
(x – 2)
2
+ 1 = 2x – 3
• LHS = (x – 2)² + 1 = x² – 4x + 4 + 1 = x²  – 4x + 5
• Therefore, (x – 2) ² + 1 = 2x – 3 can be rewritten as
• x²   – 4x + 5 =  2x – 3
• i.e., x²  – 6x + 8 = 0
• It is of the form ax² + bx + c = 0.
• Therefore, the given equation is a quadratic equation.
Another Example
x(x + 1) + 8 = (x + 2) (x – 2)
• Since x(x + 1) + 8 = x²+ x + 8 and (x + 2)(x – 2) = x2 – 4
Therefore, x² + x + 8 = x² – 4
• i.e., x + 12 = 0
• It is not of the form ax² + bx + c = 0.
• Therefore, the given equation is not a quadratic equation.
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## Mathematics (Maths) Class 10

124 videos|485 docs|105 tests

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## FAQs on Quadratic Equations Class 10 PPT

 1. What is a quadratic equation?
Ans. A quadratic equation is a second-degree polynomial equation in a single variable, usually written in the form ax^2 + bx + c = 0, where a, b, and c are constants, and 'x' represents the variable.
 2. How do you solve a quadratic equation?
Ans. Quadratic equations can be solved using various methods, such as factoring, completing the square, or using the quadratic formula. The most common method is using 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. What are the roots of a quadratic equation?
Ans. The roots of a quadratic equation are the values of 'x' which satisfy the equation and make it true. If a quadratic equation has real solutions, it will have two roots. These roots can be equal (when the discriminant is 0) or distinct (when the discriminant is greater than 0).
 4. What is the discriminant of a quadratic equation?
Ans. The discriminant of a quadratic equation is the value inside the square root in the quadratic formula, i.e., b^2 - 4ac. It helps determine the nature of the roots. If the discriminant is positive, the equation has two distinct real roots. If it is zero, the equation has two equal real roots. And if the discriminant is negative, the equation has two complex roots.
 5. How are quadratic equations used in real life?
Ans. Quadratic equations have various real-life applications, including physics, engineering, finance, and computer graphics. For example, they can be used to analyze projectile motion, design bridges and buildings, model population growth, determine profit and loss in business, or create realistic animations in video games.

## Mathematics (Maths) Class 10

124 videos|485 docs|105 tests

### Up next

 Doc | 3 pages
 Doc | 18 pages
 Video | 05:56 min
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