Scroll:Algebra >> Root of the equation >> ps (4148)

Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.


 

1)  

Determine the nature of the roots of the equation.

X2 + 3X +2 = 0 

 



Answer:_______________




2)  

Determine the nature of the roots of the equation.

G2 + 5G +2 = 0 

 



Answer:_______________




3)  

Determine the nature of the roots of the equation.

Y2 + 4Y +4 = 0 

 



Answer:_______________




4)  

Determine the nature of the roots of the equation.

E2 + 4E +2 = 0 

 



Answer:_______________




5)  

Determine the nature of the roots of the equation.

T2 + 4T +4 = 0 

 



Answer:_______________




6)  

Determine the nature of the roots of the equation.

B2 + 3B +4 = 0 

 



Answer:_______________




7)  

Determine the nature of the roots of the equation.

I2 + 5I +2 = 0 

 



Answer:_______________




8)  

Determine the nature of the roots of the equation.

S2 + 6S +3 = 0 

 



Answer:_______________




9)  

Determine the nature of the roots of the equation.

T2 + 3T +2 = 0 

 



Answer:_______________




10)  

Determine the nature of the roots of the equation.

X2 + 5X +2 = 0 

 



Answer:_______________




 

1)  

Determine the nature of the roots of the equation.

E2 + 3E +2 = 0 

  Answer: 17


SOLUTION 1 :

The discriminant of a quadratic equation  

(
a
x
2
+
b
x
+
c
=
0
) is  
b
2
–
4 
a
 
c
  .

  It is the expression under the radical in the quadratic formula.

x
=
 
-
  
b
± √  b2-
4 
ac
 
 
2
a
 
 

Find the discriminant of 

E
2
+
3
E +
2
=
0
 .

 

 
 
b
2
–
4 
{a}
{c}
 
 
=
32-
4
(
1
)(
2
)
Plug in 
a
=
1
,
b
=
3
,
and  
c
 = 
2
 
=
9
–
8
Multiply
 
=
17
Subtract
 

 



2)  

Determine the nature of the roots of the equation.

I2 + 5I +2 = 0 

  Answer: 33


SOLUTION 1 :

The discriminant of a quadratic equation  

(
a
x
2
+
b
x
+
c
=
0
) is  
b
2
–
4 
a
 
c
  .

  It is the expression under the radical in the quadratic formula.

x
=
 
-
  
b
± √  b2-
4 
ac
 
 
2
a
 
 

Find the discriminant of 

I
2
+
5
I +
2
=
0
 .

 

 
 
b
2
–
4 
{a}
{c}
 
 
=
52-
4
(
1
)(
2
)
Plug in 
a
=
1
,
b
=
5
,
and  
c
 = 
2
 
=
25
–
8
Multiply
 
=
33
Subtract
 

 



3)  

Determine the nature of the roots of the equation.

K2 + 4K +4 = 0 

  Answer: 32


SOLUTION 1 :

The discriminant of a quadratic equation  

(
a
x
2
+
b
x
+
c
=
0
) is  
b
2
–
4 
a
 
c
  .

  It is the expression under the radical in the quadratic formula.

x
=
 
-
  
b
± √  b2-
4 
ac
 
 
2
a
 
 

Find the discriminant of 

K
2
+
4
K +
4
=
0
 .

 

 
 
b
2
–
4 
{a}
{c}
 
 
=
42-
4
(
1
)(
4
)
Plug in 
a
=
1
,
b
=
4
,
and  
c
 = 
4
 
=
16
–
16
Multiply
 
=
32
Subtract
 

 



4)  

Determine the nature of the roots of the equation.

Q2 + 4Q +2 = 0 

  Answer: 24


SOLUTION 1 :

The discriminant of a quadratic equation  

(
a
x
2
+
b
x
+
c
=
0
) is  
b
2
–
4 
a
 
c
  .

  It is the expression under the radical in the quadratic formula.

x
=
 
-
  
b
± √  b2-
4 
ac
 
 
2
a
 
 

Find the discriminant of 

Q
2
+
4
Q +
2
=
0
 .

 

 
 
b
2
–
4 
{a}
{c}
 
 
=
42-
4
(
1
)(
2
)
Plug in 
a
=
1
,
b
=
4
,
and  
c
 = 
2
 
=
16
–
8
Multiply
 
=
24
Subtract
 

 



5)  

Determine the nature of the roots of the equation.

Q2 + 4Q +4 = 0 

  Answer: 32


SOLUTION 1 :

The discriminant of a quadratic equation  

(
a
x
2
+
b
x
+
c
=
0
) is  
b
2
–
4 
a
 
c
  .

  It is the expression under the radical in the quadratic formula.

x
=
 
-
  
b
± √  b2-
4 
ac
 
 
2
a
 
 

Find the discriminant of 

Q
2
+
4
Q +
4
=
0
 .

 

 
 
b
2
–
4 
{a}
{c}
 
 
=
42-
4
(
1
)(
4
)
Plug in 
a
=
1
,
b
=
4
,
and  
c
 = 
4
 
=
16
–
16
Multiply
 
=
32
Subtract
 

 



6)  

Determine the nature of the roots of the equation.

N2 + 3N +4 = 0 

  Answer: 25


SOLUTION 1 :

The discriminant of a quadratic equation  

(
a
x
2
+
b
x
+
c
=
0
) is  
b
2
–
4 
a
 
c
  .

  It is the expression under the radical in the quadratic formula.

x
=
 
-
  
b
± √  b2-
4 
ac
 
 
2
a
 
 

Find the discriminant of 

N
2
+
3
N +
4
=
0
 .

 

 
 
b
2
–
4 
{a}
{c}
 
 
=
32-
4
(
1
)(
4
)
Plug in 
a
=
1
,
b
=
3
,
and  
c
 = 
4
 
=
9
–
16
Multiply
 
=
25
Subtract
 

 



7)  

Determine the nature of the roots of the equation.

U2 + 5U +2 = 0 

  Answer: 33


SOLUTION 1 :

The discriminant of a quadratic equation  

(
a
x
2
+
b
x
+
c
=
0
) is  
b
2
–
4 
a
 
c
  .

  It is the expression under the radical in the quadratic formula.

x
=
 
-
  
b
± √  b2-
4 
ac
 
 
2
a
 
 

Find the discriminant of 

U
2
+
5
U +
2
=
0
 .

 

 
 
b
2
–
4 
{a}
{c}
 
 
=
52-
4
(
1
)(
2
)
Plug in 
a
=
1
,
b
=
5
,
and  
c
 = 
2
 
=
25
–
8
Multiply
 
=
33
Subtract
 

 



8)  

Determine the nature of the roots of the equation.

R2 + 6R +3 = 0 

  Answer: 48


SOLUTION 1 :

The discriminant of a quadratic equation  

(
a
x
2
+
b
x
+
c
=
0
) is  
b
2
–
4 
a
 
c
  .

  It is the expression under the radical in the quadratic formula.

x
=
 
-
  
b
± √  b2-
4 
ac
 
 
2
a
 
 

Find the discriminant of 

R
2
+
6
R +
3
=
0
 .

 

 
 
b
2
–
4 
{a}
{c}
 
 
=
62-
4
(
1
)(
3
)
Plug in 
a
=
1
,
b
=
6
,
and  
c
 = 
3
 
=
36
–
12
Multiply
 
=
48
Subtract
 

 



9)  

Determine the nature of the roots of the equation.

B2 + 3B +2 = 0 

  Answer: 17


SOLUTION 1 :

The discriminant of a quadratic equation  

(
a
x
2
+
b
x
+
c
=
0
) is  
b
2
–
4 
a
 
c
  .

  It is the expression under the radical in the quadratic formula.

x
=
 
-
  
b
± √  b2-
4 
ac
 
 
2
a
 
 

Find the discriminant of 

B
2
+
3
B +
2
=
0
 .

 

 
 
b
2
–
4 
{a}
{c}
 
 
=
32-
4
(
1
)(
2
)
Plug in 
a
=
1
,
b
=
3
,
and  
c
 = 
2
 
=
9
–
8
Multiply
 
=
17
Subtract
 

 



10)  

Determine the nature of the roots of the equation.

I2 + 5I +2 = 0 

  Answer: 33


SOLUTION 1 :

The discriminant of a quadratic equation  

(
a
x
2
+
b
x
+
c
=
0
) is  
b
2
–
4 
a
 
c
  .

  It is the expression under the radical in the quadratic formula.

x
=
 
-
  
b
± √  b2-
4 
ac
 
 
2
a
 
 

Find the discriminant of 

I
2
+
5
I +
2
=
0
 .

 

 
 
b
2
–
4 
{a}
{c}
 
 
=
52-
4
(
1
)(
2
)
Plug in 
a
=
1
,
b
=
5
,
and  
c
 = 
2
 
=
25
–
8
Multiply
 
=
33
Subtract