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Given two quadratic equations ax^(2)+3x-...

Given two quadratic equations `ax^(2)+3x-4=0` and `x^(2)-5x+6a=0` If the roots of equation (i) and (ii) are `alpha_(1), beta_(1)` and `alpha_(2), beta_(2)` respectively, then For which of the following set of real value of `a`, `alpha_(1),beta_(1)` and `alpha_(2),beta_(2)` are real
(A) `(-oo,-(9)/(16)]uu[(25)/(24),oo)`
(B) `(-(9)/(16),(25)/(24))-{0}`
(C) `[-(9)/(16),(25)/(24)]-{0}`
(D) `(-(1)/(4),(1)/(2))-{0}`

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