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If α , β , γ are the roots of x3 − 2 x2 + 3x − 4 = 0, then the value of α 2β2 + β2γ2+ γ2α 2 is
  • a)
    -7
  • b)
    -5
  • c)
    -3
  • d)
    0
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If α , β , γ are the roots of x3 − 2 x2 + 3x &m...
Solution:

Given:
The roots of the equation x³ - 2x² + 3x - 4 = 0 are α, β, and γ.
To find:
The value of α²β² + β²γ² + γ²α².
Explanation:
Given the roots of the equation, we have:
α + β + γ = 2
αβ + βγ + γα = 3
αβγ = 4
We need to find the value of α²β² + β²γ² + γ²α².
Using the values of α, β, and γ, we can express this as:
α²β² + β²γ² + γ²α² = (α² + β² + γ²)(α²β² + β²γ² + γ²α² - 2αβγ)
Substitute the values of α² + β² + γ² and αβγ:
α²β² + β²γ² + γ²α² = [(α + β + γ)² - 2(αβ + βγ + γα)](α²β² + β²γ² + γ²α² - 2αβγ)
α²β² + β²γ² + γ²α² = [(2)² - 2(3)](α²β² + β²γ² + γ²α² - 2(4))
α²β² + β²γ² + γ²α² = [4 - 6](α²β² + β²γ² + γ²α² - 8)
α²β² + β²γ² + γ²α² = -2(α²β² + β²γ² + γ²α² - 8)
α²β² + β²γ² + γ²α² = -2α²β² - 2β²γ² - 2γ²α² + 16
Now, substitute the given values:
α²β² + β²γ² + γ²α² = -2(4) + 16
α²β² + β²γ² + γ²α² = -8 + 16
α²β² + β²γ² + γ²α² = 8
Therefore, the value of α²β² + β²γ² + γ²α² is 8.
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If α , β , γ are the roots of x3 − 2 x2 + 3x − 4 = 0, then the value of α 2β2 + β2γ2+ γ2α 2isa)-7b)-5c)-3d)0Correct answer is option 'A'. Can you explain this answer?
Question Description
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