Class 10 Exam  >  Class 10 Notes  >  Mathematics (Maths) Class 10  >  PPT: Quadratic Equations

Quadratic Equations Class 10 PPT

Download, print and study this document offline
Please wait while the PDF view is loading
 Page 1


QUADRATIC  
EQUATIONS
Page 2


QUADRATIC  
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


QUADRATIC  
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


QUADRATIC  
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 
QUADRATIC EQUATIONS:
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


QUADRATIC  
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 
QUADRATIC EQUATIONS:
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.
Read More
124 videos|485 docs|105 tests

Up next

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.
124 videos|485 docs|105 tests
Download as PDF

Up next

Explore Courses for Class 10 exam
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Download the FREE EduRev App
Track your progress, build streaks, highlight & save important lessons and more!
Related Searches

practice quizzes

,

MCQs

,

Extra Questions

,

Free

,

ppt

,

Quadratic Equations Class 10 PPT

,

study material

,

past year papers

,

Important questions

,

Summary

,

Previous Year Questions with Solutions

,

shortcuts and tricks

,

video lectures

,

mock tests for examination

,

Sample Paper

,

Semester Notes

,

Exam

,

Quadratic Equations Class 10 PPT

,

Quadratic Equations Class 10 PPT

,

pdf

,

Objective type Questions

,

Viva Questions

;