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If the equation 3x^2 + 4ax + b = 0 has a...

If the equation `3x^2 + 4ax + b = 0` has at least one root in `(0,1)` such that `La + Mb + N = 0`, where `L, M, N` are co-prime numbers, then the value of `L + M + N + LMN` is

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To solve the problem, we need to analyze the quadratic equation given and apply the conditions provided. Let's break it down step by step. ### Step 1: Understand the Quadratic Equation The given equation is: \[ 3x^2 + 4ax + b = 0 \] We need to find conditions under which this equation has at least one root in the interval \( (0, 1) \). ### Step 2: Evaluate the Function at the Endpoints ...
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