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If alpha,beta are the zeros of the quadr...

If `alpha,beta` are the zeros of the quadratic polynomial `x^2+ax+b` and `gamma,delta` be the zeros of the polynomial `x^2-ax+(b-2)`, Given that `1/alpha+1/beta+1/gamma+1/delta=5/12` and `alphabetagammadelta=24`. Find the value of `a`.

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