Quadratic Equations Class 10 PPT

 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.