QUADRATIC EQUATIONS
Quadratic Equation
What is a quadratic equation ?
9x2 + 5x + 7 = 9
Degree 2
Quadratic Equation is an equation in one variable with degree 2
Quadratic Equation
Degree 5
Not a Quadratic Equation
Not a Quadratic Equation
Highest index of variable
Highest index is 2
General form of Quadratic Equation:-
x2 +
x +
= 0
a
b
c
where a, b and c are real numbers;
a ≠ 0
If a = 0, then
0x2 + bx + c = 0
∴ bx + c = 0
Degree 1
Which is not a quadratic equation
Coefficient of square term as a
Zero is a real no
If, b = 0
If, c = 0
Degree 2
A term with
index 2
A term with
index 1
Then,
= 0
constant term
as c
Coefficient of middle term as b
Then, equation will be ax2 + c = 0
It is a Quadratic Equation
Then, equation will be ax2 + bx = 0
It is a Quadratic Equation
Think it over:
What if b=0,c=0.
two variables
Highest index is 2
Degree 2
Highest index is 5
1) Which of the following are quadratic equations?
ii) (y – 2) (y + 2) = 0
(y – 2) (y + 2) = 0
∴ (y)2 – (2)2 = 0
∴ y2 – 4 = 0
∴ y2 + 0y – 4 = 0
The given equation is in the form of ay2 + by + c = 0
So it is a quadratic equation in variable y
Sol:
i) 11 = - 4x2 – x3
Sol:
11 = - 4x2 – x3
∴ x3 + 4x2 + 11 = 0
The given equation is not in the form of ax2 + bx + c = 0 .
So it is not a quadratic equation.
(a – b)(a + b) = a2 – b2
Middle term is missing
Represent Middle term as 0y
Highest index of variable is 2
Arrange Equation
such that we get
RHS as 0
Highest index of variable is 3