- This is an assessment test.
- To draw maximum benefit, study the concepts for the topic concerned.
- Kindly take the tests in this series with a pre-defined schedule.

## Algebra: Quadratic Equations Test-2

Congratulations - you have completed

*Algebra: Quadratic Equations Test-2*.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 |

The minimum value of (x -2) (x-9) is

-11/4 | |

49/4 | |

0 | |

-49/4 |

Question 1 Explanation:

$ \displaystyle \begin{array}{l}\left( x\text{ }-2 \right)\text{ }\left( x-9 \right)\\={{x}^{2}}-11x+18\\={{x}^{2}}-2.\frac{11}{2}x+\frac{121}{4}-\frac{49}{4}\\={{(x-\frac{11}{2})}^{2}}-\frac{49}{4}\end{array}$

The minimum value of the square is 0. The minimum value is -49/4

The minimum value of the square is 0. The minimum value is -49/4

Question 2 |

One of the factors of the expression

$ \displaystyle 4\sqrt{3}{{x}^{2}}+5x-2\sqrt{3}$

$ \displaystyle 4\sqrt{3}{{x}^{2}}+5x-2\sqrt{3}$

$ \displaystyle 4x+\sqrt{3}$ | |

$ \displaystyle 4x+3$ | |

$ \displaystyle 4x-3$ | |

$ \displaystyle 4x-\sqrt{3}$ |

Question 2 Explanation:

$ \displaystyle \begin{array}{l}4\sqrt{3}\,\,\,{{x}^{2}}+5x-2\sqrt{3}\\=4\sqrt{3}\,\,\,{{x}^{2}}+8x-3x-2\sqrt{3}\\=4x\left( \sqrt{3}\,\,\,x+2 \right)-\sqrt{3}\left( \sqrt{3}x+2 \right)\\=\left( 4x-\sqrt{3} \right)\left( \sqrt{3}x+2 \right)\end{array}$

Question 3 |

$ \displaystyle \begin{array}{l}\sqrt{x}=\sqrt{3}-\sqrt{5},\,\,\,\\then\,\,\,the\,\,\,value\,\,\,of\,\,\,\\{{x}^{2}}-16x+6\,\,is\end{array}$

0 | |

-2 | |

2 | |

4 |

Question 3 Explanation:

$ \sqrt{x}=\sqrt{3}-\sqrt{5}$

$ \begin{array}{l}x=3+5-2\sqrt{15}\\=>x=8-2\sqrt{15}\\=>{{x}^{2}}=64+60-32\sqrt{15}=124-32\sqrt{15}\\Thus\,{{x}^{2}}-16x+6\\=124-32\sqrt{15}-16(8-2\sqrt{15})+6\\=124-32\sqrt{15}-128+32\sqrt{15}+6\\=2\end{array}$

$ \begin{array}{l}x=3+5-2\sqrt{15}\\=>x=8-2\sqrt{15}\\=>{{x}^{2}}=64+60-32\sqrt{15}=124-32\sqrt{15}\\Thus\,{{x}^{2}}-16x+6\\=124-32\sqrt{15}-16(8-2\sqrt{15})+6\\=124-32\sqrt{15}-128+32\sqrt{15}+6\\=2\end{array}$

Question 4 |

$ \displaystyle x=\sqrt[3]{5}+2,\,\,then\,\,\,the\,\,value\,\,\,of\,\,\,{{x}^{3}}-6{{x}^{2}}+12x-13\,\,is$

-1 | |

1 | |

4 | |

0 |

Question 4 Explanation:

$ \begin{array}{l}\,{{x}^{3}}-6{{x}^{2}}+12x-13\\=\,{{x}^{3}}-3.2.{{x}^{2}}+{{3.2}^{2}}x-{{2}^{3}}-5\\={{(x-2)}^{3}}-5\\={{(\sqrt[3]{5}+2-2)}^{3}}-5\\=5-5\\=0\end{array}$

Question 5 |

A boy was asked of his age by his friend. The boy said, "The number you get when you subtract 25 times my age from twice the square of my age will be thrice your age." If the friend's age is 14, then the age of the boy is?

28 yr | |

21 yr | |

14 yr | |

25 yr |

Question 5 Explanation:

$ \begin{array}{l}Let\,the\,age\,be\,x.\\2{{x}^{2}}-25x=3X14\\=>2{{x}^{2}}-25x-42=0\\=>(x-14)(2x-3)=0\\=>x=14\,\end{array}$

Rejecting the negative solution, we find that the age is 14 years.

Rejecting the negative solution, we find that the age is 14 years.

Once you are finished, click the button below. Any items you have not completed will be marked incorrect.

There are 5 questions to complete.

List |