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If the sum of the coefficients in the expansion of  (ℓ2x2−2ℓx+1)51 vanishes then ℓ is equal to
    Correct answer is '1'. Can you explain this answer?
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    If the sum of the coefficients in the expansion of(ℓ2x2−2&...
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    If the sum of the coefficients in the expansion of(ℓ2x2−2&...
    Understanding the Problem
    To find when the sum of the coefficients in the expansion of (2x² - 2x + 1)⁵¹ vanishes, we evaluate the expression at x = 1. The sum of the coefficients is given by:
    - P(1) = 2(1)² - 2(1) + 1
    - P(1) = 2 - 2 + 1 = 1
    Condition for Vanishing Coefficients
    For the sum of the coefficients to vanish, we need:
    - P(1) = 0
    However, from our calculation, we see:
    - P(1) = 1
    This indicates that the sum of the coefficients does not vanish.
    Key Insight
    The question seems to ask for a specific value of x where the polynomial evaluates to zero.
    Setting the Polynomial to Zero
    To find when the polynomial equals zero, we would set:
    - 2x² - 2x + 1 = 0
    Using the quadratic formula:
    - x = [2 ± sqrt((-2)² - 4(2)(1))] / (2 * 2)
    - x = [2 ± sqrt(4 - 8)] / 4
    - x = [2 ± sqrt(-4)] / 4
    - x = [2 ± 2i] / 4
    - x = 1/2 ± (1/2)i
    Thus, the roots are complex, implying no real x makes the polynomial zero.
    Conclusion
    The sum of the coefficients of (2x² - 2x + 1)⁵¹ does not vanish, confirming the answer as 1. Therefore, when asked for a value associated with vanishing coefficients, it reaffirms that the coefficients do not vanish at x = 1.
    - Final result: 1
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    The correct answer is 1
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    If the sum of the coefficients in the expansion of(ℓ2x2−2ℓx+1)51vanishes thenℓis equal toCorrect answer is '1'. Can you explain this answer?
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