P(X) = 4✓3X²+5X-2✓3

=> 4✓3X² +8X-3X-2✓3

=> 4X(✓3X+2) -✓3(✓3X+2)

=> (✓3X+2)(4X-✓3) = 0

=> (✓3X +2)= 0 OR (4X-✓3) = 0

=> X = -2/✓3 OR X = ✓3/4

-2/✓3 and ✓3/4 are the two zeros of the given polynomial.

Let Alpha = -2/✓3 and beta = ✓3/4

Relationship between the zeros and Coefficient.

Sum of zeros = (Alpha + Beta) = -2/✓3 + ✓3/4 = -8+3/4✓3 = -5/4✓3 = - ( Coefficient of X/Coefficient of X²)

And,

Product of zeros = (Alpha × Beta) = -2/✓3 × ✓3/4 = -2✓3/4✓3 = Constant term/Coefficient of X².

When the power in a country is divided into the Central and the State government, it is called a federal division of power. In a federal set up, while the Central government looks after the administration of the entire country, the state governments look into the administration of their respective states.

नगरपालिका चौराहे पर नेता जी सुभाष चंद्र बोस की मूर्ति स्थापित करना चाहती थी। नगरपालिका का मूर्ति बनाने का बजट सीमित था इसलिए उन लोगों ने मूर्ति बनाने का कार्य स्थानीय स्कूल के ड्राइंग मास्टर मोतीलाल जी को दे दिया। मास्टर मोतीलाल को जब यह कार्य मिला तो उन्हें बहुत खुशी हुई। उन्होंने नगरपालिका के सदस्यों को यह विश्वास दिलाया कि वह एक महीने के अंदर मूर्ति तैयार कर देंगे। इस प्रकार का कार्य मिलने से कलाकार में नया उत्साह जागृत हुआ। उन्हें ऐसा लगा कि नगरपालिका ने उनकी कला को प्रोत्साहन देने के लिए यह कार्य उन्हें सौंपा है। इसीलिए उन्होंने अपनी बात के अनुसार एक महीने में मूर्ति पूरी कर दी।

Assuming the question as

What were the 'new coins' to Lencho? 

Answer:

Lencho’s crops were ready for harvest. However, they required a good downpour before harvesting. After a downpour, he could sell the harvest and get money. That is why he compared the raindrops to ‘new coins

Let √2 be a rational number 

Therefore, √2= p/q  [ p and q are in their least terms i.e., HCF of (p,q)=1 and q ≠ 0

On squaring both sides, we get 
                   p²= 2q²                                                                                    ...(1)
Clearly, 2 is a factor of 2q²
⇒ 2 is a factor of p²                                                                    [since, 2q²=p²]
⇒ 2 is a factor of p

 Let p =2 m for all m ( where  m is a positive integer)

Squaring both sides, we get 
            p²= 4 m²                                                                                          ...(2)
From (1) and (2), we get 
           2q² = 4m²      ⇒      q²= 2m²
Clearly, 2 is a factor of 2m²
⇒       2 is a factor of q²                                                      [since, q² = 2m²]
⇒       2 is a factor of q 

Thus, we see that both p and q have common factor 2 which is a contradiction that H.C.F. of (p,q)= 1

     Therefore, Our supposition is wrong

Hence √2 is not a rational number i.e., irrational number..

Gas is one of the four fundamental states of matter (the others being solid, liquid, and plasma). A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or compound molecules made from a variety of atoms (e.g. carbon dioxide).

(i) A multipurpose project is that which fulfils a variety of purposes at the same time, for example – irrigation, generation of electricity, flood control, fish breeding, soil conservation, etc.
(ii) It would integrate development of agriculture and the village economy with rapid industrialisation and the growth of urban economy.

Public interest groups promote collective rather than selective good. They aim to help groups other than their own members. Trade Unions, Students’ Union, Ex-Armymen Association, etc. are examples of public interest groups.

FEDERALISM is practiced in India by, The creation of Linguistic States was the first and a major test for democratic politics in our country. In 1947, the boundaries of several old States were changed in order to create new States. This was done to ensure that people who spoke the same language lived in the same State.

Romanticism (also known as the Romantic era) was an artistic, literary, musical and intellectual movement that originated in Europe towards the end of the 18th century, and in most areas was at its peak in the approximate period from 1800 to 1890. Examples of contribution of culture to the growth of nationalism in Europe are   (i) The idea of a nation can be created through stories, poets and writings. Music too can help in expressing nationalist feelings or sentiments.   (ii) Romanticism, a cultural movement which emerged in Europe, sought to develop a particular form of nationalist sentiments or national feelings. The main aim of romantic artists was to create a sense of a shared collective heritage and a common cultural past.   (iii) Language also played an important role in developing the national sentiments or nationalist feeling, e.g., in Poland, language began to be used as a weapon of national resistance. The wide scale use of Polish language came to be seen as a symbol of struggle against national dominance.  

Trigonometry is a branch of mathematics dealing with relations involving lengths and angles of triangles. It can, in a simpler manner, be called the study of triangles. The angles are either measured in degrees or radians.

In a federal form of government, the central government shares its powers with the various constituent units of the country. For example, in India, power is divided between the government at the Centre and the various State governments.