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## Algebra Level 2 Test 8

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*Algebra Level 2 Test 8*.You scored %%SCORE%% out of %%TOTAL%%.You correct answer percentage: %%PERCENTAGE%% .Your performance has been rated as %%RATING%% Your answers are highlighted below.

Question 1 |

If x = 2 + 2

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

B | 2 |

C | 1 |

D | 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

Letâ€™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 donâ€™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

Letâ€™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 donâ€™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 | 3x ^{2} â€“ 4x +5 |

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

C | (x â€“ 1)(2x â€“ 5) |

D | 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 }â€“ 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 }Â isA | 36 |

B | 24 |

C | 12 |

D | 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}â€“ 2ab = 24Question 4 |

If (x+1) is factor of 2x

^{3}â€“ ax^{2}â€“ (2a â€“ 3 )x +2, then the value of â€˜aâ€™ isA | 3 |

B | 2 |

C | 3/2 |

D | Â½ |

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}â€“ ax^{2}â€“ (2a â€“ 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 Â 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 varunâ€™s son = q years

Therefore

p = 3q

(p -15) = 9(q â€“ 15)

(p â€“ 9q) = -120â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦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 varunâ€™s son = q years

Therefore

p = 3q

(p -15) = 9(q â€“ 15)

(p â€“ 9q) = -120â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦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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