QUADRATIC EQUATIONS
. Stating whether the given equation is a
Quadratic Equation or not ?
Q.) Check whether the following are quadratic equations :
(iv) (x – 3) (2x + 1) = x (x + 5)
Sol :
x
(2x + 1)
∴
(x – 3) (2x + 1) = x (x + 5)
– 3
(2x + 1)
=
x2
+ 5x
2x2
∴
+ x
– 6x
– 3
=
x2
+ 5x
∴
2x2
– 5x
– 3
=
x2
+ 5x
i.e.
x2
– 10x
– 3
=
0
Arrange Equation
such that we get
RHS as 0
The given equation is in the form of ax2 + bx + c = 0.
So it is a quadratic equation.
Highest index of variable is 2
∴
2x2
– 5x
– 5x
=
– x2
– 3
0
EX 4.1 1(IV)
homework
Q.) Check whether the following are quadratic equations :
(v) (2x – 1) (x – 3) = (x + 5) (x – 1)
Sol :
2x
(x – 3)
∴
(2x – 1) (x – 3) = (x + 5) (x – 1)
– 1
(x – 3)
=
x
(x – 1)
+ 5
(x – 1)
2x2
∴
– 6x
– x
+ 3
=
x2
– x
+ 5x
– 5
2x2
∴
– 7x
+ 3
=
x2
+ 4x
– 5
x2
i.e.
– 11x
+ 8
= 0
The given equation is in the form of ax2 + bx + c = 0.
So it is a quadratic equation.
Highest index of variable is 2
Arrange Equation
such that we get
RHS as 0
2x2
∴
– 7x
+ 3
=
– x2
– 4x
+ 5
0
EX 4.1 1(V)
Q.) Check whether the following are quadratic equations :
(vi) x² + 3x + 1 = (x – 2)²
Sol :
x² + 3x + 1 = (x – 2)²
∴
x² + 3x + 1
=
x²
– 4x
+ 4
i.e.
7x
– 3
= 0
The given equation is not in the form of ax2 + bx + c = 0.
So it is not a quadratic equation.
(a + b)2 = a2 + 2ab + b2
Arrange equation such that we get RHS = 0
∴
3x
=
0
+ 4x
- 4
+ 1
EX 4.1 1(VI)