Examples for Practice (2.5)
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1. Find the value of the discriminant:
1.
x
2
+ 4
x
+ 1 = 0
Answer:
12
2. 3
x
2
+ 2
x
− 1 = 0
Answer:
16
3.
x
2
+
x
+ 1 = 0
Answer:
− 3
4.
3
x
2
+
2
2
x
-
2
3
=
0
Answer:
32
5. 4
x
2
−
kx
+ 2 = 0
Answer:
k
2
− 32
6.
x
2
+ 4
x
+
k
= 0
Answer:
16 − 4
k
7. 2
y
2
− 4
y
+ 3 = 0
Answer:
− 8
8.
3
x
2
-
2
x
+
1
3
=
0
Answer:
0
2. Determine the nature of the roots of the following equations from their discriments:
1.
y
2
− 4
y
+ 1 = 0
Answer:
Real and Equal
2.
y
2
− 6
y
− 2 = 0
Answer:
Real and Unequal
3.
y
2
+ 8
y
+ 4 = 0
Answer:
Real and Unequal
4. 2
y
2
+ 5
y
− 3 = 0
Answer:
Real and Unequal
5. 3
y
2
+ 9
y
+ 4 = 0
Answer:
Real and Unequal
6.
2
x
2
+
5
3
x
+
16
=
0
Answer:
Not Real
7. 2
x
2
− 3
x
+ 5 = 0
Answer:
Not Real
8.
3
x
2
-
4
3
x
+
4
=
0
Answer:
Real and Equal
9. 2
x
2
− 6
x
+ 3 = 0
Answer:
Real and Unequal
3. Find the value of
k
for which the given equations have real and equal roots:
1. (
k
− 12)
x
2
+ 2(
k
− 12)
x
+ 2 = 0
Answer:
14
2.
k
2
x
2
− 2(
k
− 1)
x
+ 4 = 0
Answer:
− 1 or
1
3
3. 2
x
2
+
kx
+ 3 = 0
Answer:
2
6
or
-
2
6
4.
kx
(
kx
− 2) + 6 = 0
Answer:
6
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This page was last modified on
06 March 2021 at 20:34