Question 1

Accepted Answer

According to the Fundamental Theorem of Arithmetic, the prime factorisation of a composite number is unique up to the order of the factors. (गणित के मौलिक प्रमेय के अनुसार, एक भाज्य संख्या का अभाज्य गुणनखंडन गुणनखंडों के क्रम तक अद्वितीय होता है।)

Question 2

Accepted Answer

The prime factorisation of 196 is 2² × 7². The exponents are 2 and 2. Their sum is 2 + 2 = 4. (196 का अभाज्य गुणनखंडन 2² × 7² है। घातांक 2 और 2 हैं। इनका योग 2 + 2 = 4 है।)

Question 3

Accepted Answer

The product of a non-zero rational number and an irrational number is always irrational. (एक अशून्य परिमेय संख्या और एक अपरिमेय संख्या का गुणनफल सदैव अपरिमेय होता है।)

Question 4

Accepted Answer

Polynomial is k[x² - (Sum)x + (Product)]. x² - (-3)x + 2 = x² + 3x + 2. (बहुपद k[x² - (योग)x + (गुणनफल)] है। x² - (-3)x + 2 = x² + 3x + 2.)

Question 5

Accepted Answer

Let roots be α, 2α. Sum 3α = 3 => α=1. Product 2α² = k => k = 2(1)² = 2. (माना मूल α, 2α हैं। योग 3α = 3 => α=1. गुणनफल 2α² = k => k = 2(1)² = 2.)

Mathematics (गणित)

Mathematics (गणित)

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