Module-1 Algebra Quadratic Equations Worksheet With Answers Page 2
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14MODULE -
1
Quadratic Equations
Algebra
Example 6.1:
Which of the following equations are quadratic equations?
2
2
(i) 3x
= 5
(ii) x
+ 2x + 3 = 0
3
2
(iii) x
+ 1 = 3x
(iv) (x + 1) (x + 3) = 2x + 1
Notes
1
5
+
=
x
+
+
=
(v)
(v)
2
x
x
1
0
x
2
Solution:
2
2
2
(i) It is a quadratic equation since 3x
= 5 can be written as 3x
– 5 = 0 and 3x
– 5 is a
quadratic polynomial.
2
2
(ii) x
+ 2x + 3 = 0 is a quadratic equation as x
+ 2x + 3, is a polynomial of degree 2.
(iii) x
3
+ 1 = 3x
2
can be written as x
3
– 3x
2
+ 1 = 0. LHS is not a quadratic polynomial
since highest exponent of x is 3. So, the equation is not a quadratic equation.
(iv) (x + 1) (x + 3) = 2x + 1 is a quadratic equation, since (x + 1) (x + 3) = 2x + 1 can be
written as
2
x
+ 4x + 3 = 2x + 1
or x
2
+ 2x + 2 = 0
Now, LHS is a polynomial of degree 2, hence (x + 1) (x + 3) = 2x + 1 is a quadratic
equation.
1
5
+
=
x
(v)
is not a quadratic equation.
x
2
However, it can be reduced to quadratic equation as shown below:
1
5
+
=
x
x
2
+
2
x
1
5
=
≠
x ,
0
or
x
2
+ 1) = 5x , x ≠ 0
2
or 2(x
– 5x + 2 = 0, x ≠ 0
2
or 2x
+
+
=
+
+
(vi)
is not a quadratic equation as
is not a quadratic
2
2
x
x
1
0
x
x
1
polynomial (Why?)
Mathematics Secondary Course
171
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