Quadratic Equations Worksheet With Answer Key Page 2
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1
2
3
4
5
6
72
= (3)
– 4. 2. (-4)
= 9 + 32
= 41 > 0.
Here we got the final result as a non-perfect square and positive. So it indicates that
the given equation must give two roots which are irrational and unequal.
Example3:
2
Write the nature of roots of 2x
+ 3x + 5 = 0
Solution:
2
Comparing the given equation with ax
+ bx + c = 0, we get
a = 2, b = 3 and c = 5.
Now
2
∆ = b
- 4ac
2
= (3)
– 4. 2. (5)
= 9 - 40
= - 31< 0.
Here we got the final result as a negative. So it indicates that the given equation
must give two roots which are imaginary and unequal.
Example4:
2
Write the nature of roots of 2x
- 4x + 2 = 0
Solution:
2
Comparing the given equation with ax
+ bx + c = 0, we get
a = 2, b = -4 and c = 2.
Now
2
∆ = b
- 4ac
2
= (- 4)
– 4. 2. (2)
= 16 - 16
= 0
Here we got the final result zero. So it indicates that the given equation must give
two roots which are rational and equal. That is, the roots are repeated.
Example 5:
2
If the equation x
+ (k+2)x + 2k = 0 has equal roots, find the value of k.
Solution:
2
comparing the given equation with ax
+bx+c=0
a = 1, b = k + 2, c = 2k
since the roots are equal;
2
b
- 4ac = 0
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