Correct Answer: D. nx\(^2\) - mx - 1 = 0

Explanation

x\(^2\) + mx - n = 0

a = 1, b = m, c = -n

α + β = \(\frac{-b}{a}\) = \(\frac{-m}{1}\) = -m

αβ = \(\frac{c}{a}\) = \(\frac{-n}{1}\) = -n

the roots are = \(\frac{1}{α}\) and \(\frac{1}{β}\)

sum of the roots = \(\frac{1}{α}\) + \(\frac{1}{β}\)

\(\frac{1}{α}\) + \(\frac{1}{β}\) = \(\frac{α+β}{αβ}\)

α + β = -m

αβ = -n

\(\frac{α+β}{αβ}\) = \(\frac{-m}{-n}\) → \(\frac{m}{n}\)

product of the roots = \(\frac{1}{α}\) * \(\frac{1}{β}\)

\(\frac{1}{α}\) + \(\frac{1}{β}\) = \(\frac{1}{αβ}\) → \(\frac{1}{-n}\)

x\(^2\) - (sum of roots)x + (product of roots)

x\(^2\) - ( m/n )x + ( 1/-n ) = 0

multiply through by n

nx\(^2\) - mx - 1 = 0

Explanation

(a) Legitimacy is a political concept which has to do with the citizens' approval, acceptance and recognition of the rights of their political leaders to govern. A government is considered legitimate if it comes to power not through coup or appointments, but through constitutional means. Therefore, elected governments are legitimate. However, it is argued in some quarters that the military in government may attain legitimacy if popular policies are made by it.

(b) Factors that can sustain Legitimacy are:

(i)Good Stable government: If the government policies are good, the people will continue to have trust and confidence in such governments, for example in the areas of providing social amenities and infrastructure, maintenance of law and order, obeying the provisions of the constitution, etc.

(ii)Reliable leadership:Legitimacy may be ascribed to a leader that performs creditably in office.

(iii)Periodic elections: Free and fair elections produce legitimacy. Periodic elections will help to keep it alive.

(iv)Broad based political participation: If political appointments cut across sections of the society, this can strengthen legitimacy in such systems.

(v) Regard for customs and traditions:If the government regards customs and traditions of the people, legitimacy could be sustained, for e.g. heredity is maintained in Benin Monarch, British Monarch , etc.

(vi)Ideology: If the ruling government upholds the principle of the state ideology, this can help to sustain legitimacy, e.g Capitalism in U.S.A.

Correct Answer: D. the profit motive outweighs public interest

Correct Answer: B. 37.9

Explanation

Another word for mean is average. To find the average of this set of numbers, add them up, then divide by the amount of numbers in the set. In this case there are 7 numbers in the set, meaning we will divide our answer by 7. (41+38+27+42+35+38+44)/7=265/7=37.9

Correct Answer: D. is inversely related to the price level

Explanation

Value of money is what one unit of money can buy and the price level is the average of prices of all the goods and services within an economy. So when the price level increases the value of money goes down and vise versa. Hence the relationship between price level in an economy and the value of money is inverse.

Correct Answer: A. a satire

Correct Answer: B. Ordinary shares

Correct Answer: d) 774

Correct Answer: B. N2,400

Correct Answer: A) I and II only