Quadratic function

It is given a quadratic function y = -4x²+5x+c with unknown coefficient c. Determine the smallest integer c for which the graph of f intersects the x-axis at two different points.

Correct result:

c =  0

Solution:

$$\begin{gathered} D=b^2-4ac>0 \\ {\displaystyle \frac{b^2}{4a}}>c \\ {\displaystyle \frac{5^2}{4(-4)}}>c \\ -1.5625>c;c\min \\ c=0 \end{gathered}$$

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