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## Algebra Level 2 Test 8

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Question 1 |

If x = 2 + 2

^{2/3}+ 2^{1/3}then the value of x^{3}- 6x^{2}+ 6x is ?3 | |

2 | |

1 | |

None of these |

Question 1 Explanation:

Given that x = 2 + 2

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 x

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)

^{2/3}+ 2^{1/3}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 x

^{3}- 6x^{2}+ 6x = -9So 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?

3x ^{2} – 4x +5 | |

x ^{2} + x + 4 = 0 | |

(x – 1)(2x – 5) | |

2x ^{2} - 3x + 4 = 0 |

Question 2 Explanation:

In general the roots of the equation ax

if b

so on checking all options, option number (d) has real roots

^{2}+ by + c = 0 are realif b

^{2 }– 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 x

^{2}- 6x + 6 = 0, then what will be the value of a^{2}+b^{2 }is36 | |

24 | |

12 | |

7 |

Question 3 Explanation:

We know that (a+b)

So the sum of roots is given by =a+ b = 6

Product of the roots is given by = ab = 6

Therefore a

^{2}= a^{2}+ b^{2}+ 2abSo the sum of roots is given by =a+ b = 6

Product of the roots is given by = ab = 6

Therefore a

^{2}+ b^{2}= (a+b)^{2}– 2ab = 24Question 4 |

If (x+1) is factor of 2x

^{3}– ax^{2}– (2a – 3 )x +2 , then the value of ‘a’ is3 | |

2 | |

3/2 | |

½ |

Question 4 Explanation:

Since the factor of the given expression

2x

Therefore x+1=0

x = -1

Put the value of x in the expression

We will get a = 3

2x

^{3}– ax^{2}– (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?

45 years | |

60 years | |

75 years | |

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

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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