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Question

Find the range of a for which :
(a) ax2+3x+4>0 xR (b) ax2+4x2<0 xR

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Solution

(a)ax2+3x+4>0forallxϵRD<094a×4<0916a<016a>9a>34,aϵ(34,)
(b)ax2+4x2<0D<016+4×a×2<016+8a<08a<16a<2,aϵ(,2)

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