If a x^2+b x+c(a 1 & a, b, c are integers ) is equal to p for two distinct integral values of x, p prime, then a x^2+b x+c cannot be equal to 2 p for -

Step-by-step solution

Let m , n I satisfy ax ^2+ bx + c = p m + n =- b a mn = c - p a Let k I such that aligned & ak ^2+ bk + c =2 p & ak ^2- a ( m + n ) k + amn = p aligned aligned & a( k - m )( k - n )= p & non-prime = prime aligned a contradiction Hence no integral value of x