In vertices of \( \triangle A B C \) lie on \( y=f(x)=a x^{2}+b x+c \). The \( \triangle A B C \...

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In vertices of \( \triangle A B C \) lie on \( y=f(x)=a x^{2}+b x+c \). The \( \triangle A B C \) is right-angled isosceles triangle whose hypotenuse \( A C=4 \sqrt{2} \) units.
Number of integral values of \( k \) for which one roots of \( f(x)=0 \) is more than \( k \) and other less than \( k \)
(a) 6
(b) 5
(c) 4
(d) 7
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