Algebra: Quadratic Equations Test-1

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Algebra: Quadratic Equations Test-1

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Question 1

$\begin{array}{l}If\,\,p=99,\,\\then\,\,value\,\,of\,\,\,p\left( {{p}^{2}}+3p+3 \right)is\end{array}$

A	999
B	9999
C	99999
D	999999

Question 1 Explanation:

$\begin{array}{l}p\left( {{p}^{2}}+3p+3 \right)\\=99\left( {{99}^{2}}+3X99+3 \right)\\=99\left( 9801+297+3 \right)\\=99(9801+300)\\=99(10101)\\=999999\end{array}$

Question 2

If p= 999,
then the value of

$\displaystyle \sqrt[3]{p\left( {{p}^{2}}+3p+3 \right)+1}$ is

A	1000
B	999
C	998
D	1002

Question 2 Explanation:

$\sqrt[3]{p\left( {{p}^{2}}+3p+3 \right)+1}$

$=\sqrt[3]{999\left( 1001001 \right)+1}$

$\displaystyle \begin{array}{l}=\sqrt[3]{999999999+1}\\=\sqrt[3]{1000000000}\\=1000\end{array}$

Question 3

If p=101,
then the value of

$\displaystyle \sqrt[3]{p\left( {{p}^{2}}-3p+3 \right)-1}$ is

A	100
B	101
C	102
D	1000

Question 3 Explanation:

$\sqrt[3]{p\left( {{p}^{2}}-3p+3 \right)-1}$

$\displaystyle \begin{array}{l}\sqrt[3]{101\left( {{101}^{2}}-3X101+3 \right)-1}\\=\sqrt[3]{101\left( 10201-300 \right)-1}\\=\sqrt[3]{1000000}\\=100\end{array}$

Question 4

If p=124,

$latex \displaystyle \sqrt[3]{p\left( {{p}^{2}}+3p+3 \right)+1}$ =?

A	5
B	7
C	123
D	125

Question 4 Explanation:

$\sqrt[3]{p\left( {{p}^{2}}+3p+3 \right)+1}$

$\displaystyle \begin{array}{l}\sqrt[3]{{{p}^{3}}+3{{p}^{2}}+3p+1}\\=p+1\\=125\end{array}$

Question 5

$\displaystyle \begin{array}{l}If\,x=\sqrt{\frac{\sqrt{5}+1}{\sqrt{5}-1}}\\Then\,\,\,5{{x}^{2}}-5x-1=?\end{array}$

A	0
B	3
C	4
D	5

Question 5 Explanation:

$\begin{array}{l}x=\sqrt{\frac{\sqrt{5}+1}{\sqrt{5}-1}}\\{{x}^{2}}=\frac{\sqrt{5}+1}{\sqrt{5}-1}\\=>{{x}^{2}}=\frac{{{(\sqrt{5}+1)}^{2}}}{4}\\=>4{{x}^{2}}={{(\sqrt{5}+1)}^{2}}=6+2\sqrt{5}\\=>{{x}^{2}}=\frac{6+2\sqrt{5}}{4}\\5{{x}^{2}}-5x-1\\=\frac{30+10\sqrt{5}-10\sqrt{5}-10-4}{4}\\=\frac{16}{4}\\=4\end{array}$

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