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:

D=b24ac>0 b24a>c 524(4)>c 1.5625>c;cmin c=0D = b^2 -4ac >0 \ \\ \dfrac{ b^2}{4a} > c \ \\ \dfrac{ 5^2}{4 (-4)} > c \ \\ -1.5625 > c; c \min \ \\ c = 0

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