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The number of integer values of x such t...

The number of integer values of x such that `|x-2|+|x+3| >|2x+1|...`

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Let f (x) =ax ^(2) +bx+c, where a,b,c are integers and a gt 1. If f (x) takes the value p, a prime for two distinct integer values of x, then the number of integer values of x for which f (x) takes the value 2p is :

Let f (x) =ax ^(2) +bx+c, where a,b,c are integers and a gt 1 . If f (x) takes the value p, a prime for two distinct integer values of x, then the number of integer values of x for which f (x) takes the value 2p is :