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Algebra Level 2 Test 8

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Question 1
If x = 2 + 22/3 + 21/3 then the value of x3 - 6x2 + 6x is ?
A
3
B
2
C
1
D
None of these
Question 1 Explanation: 
Given that x = 2 + 22/3 + 21/3
Since the value of x is greater than 2 so we will use hit and trial method
Let’s check the equation with 2 and 3
Therefore
For the value of x = 2 the result will be = -4
For the value of x = 3 the value of expression x3 - 6x2 + 6x = -9
So by these two values we can say that as the values decreases as the of x increases.
The value of the expression becomes negative and we don’t have any negative value in the answer options
So the right answer is option (d)
Question 2
Which of the following equations has real roots?
A
3x2 – 4x +5
B
x2 + x + 4 = 0
C
(x – 1)(2x – 5)
D
2x2 - 3x + 4 = 0
Question 2 Explanation: 
In general the roots of the equation ax2 + by + c = 0 are real
if b2 – 4ac always greater than equal to 0,
so on checking all options, option number (d) has real roots
Question 3
If a and b are the roots of the equation x2 - 6x + 6 = 0, then what will be the value of a2 +b2  is
A
36
B
24
C
12
D
7
Question 3 Explanation: 
We know that (a+b)2 = a2 + b2 + 2ab
So the sum of roots is given by =a+ b = 6
Product of the roots is given by = ab = 6
Therefore a2 + b2 = (a+b)2 – 2ab = 24
Question 4
If (x+1) is factor of 2x3 – ax2 – (2a – 3 )x +2 , then the value of ‘a’ is
A
3
B
2
C
3/2
D
½
Question 4 Explanation: 
Since the factor of the given expression
2x3 – ax2 – (2a – 3 )x +2 is given i.e. (x+1)
Therefore x+1=0
x = -1
Put the value of x in the expression
We will get a = 3
Question 5
The age of Varun  is 3 times that of his son. 15 years ago the Varun was 9 times as old as his son. What will be the age of the Barun after 15 years?
A
45 years
B
60 years
C
75 years
D
65 years
Question 5 Explanation: 
Let the present age of varun = p years
Let the present age of varun’s son = q years
Therefore
p = 3q
(p -15) = 9(q – 15)
(p – 9q) = -120………………………………………………1
Put the value of p in the above equation 1
So we get the value of q = 20 and p= 60
Therefore the age of Varun after 15 years = 75 years
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