The quadratic function f [x] = x ^ 2 + X + a [A. > 0] is known if f [M]

The quadratic function f [x] = x ^ 2 + X + a [A. > 0] is known if f [M]

F (x) = x square + X + a = x (x + 1) + A
∵f(m)<0
∴f(m)=m(m+1)+a<0
That is m (M + 1) < - A
And ∵ a > 0, and m < m + 1
∴m<0,m+1>0
(M + 1) square ≥ 0
Ψ f (M + 1) = (M + 1) square + (M + 1) + a > 0
That is, f (M + 1) > 0