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For what value of n, the quadratic equat...

For what value of n, the quadratic equation `3^(n)x^(2)+54x+81^(n)=0` have coincident roots?

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To find the value of \( n \) for which the quadratic equation \( 3^n x^2 + 54x + 81^n = 0 \) has coincident roots, we need to use the condition that the discriminant of the quadratic equation must be equal to zero. ### Step-by-Step Solution: 1. **Identify the coefficients**: The given quadratic equation is in the form \( ax^2 + bx + c = 0 \), where: - \( a = 3^n \) - \( b = 54 \) ...
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