For the quadratic polynomial \( f(x)=4 x^{2}-8 k x+k \), the statements which hold good are (a) ...

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For the quadratic polynomial \( f(x)=4 x^{2}-8 k x+k \), the statements which hold good are
(a) there is only one integral \( k \) for which \( f(x) \) is non-negative \( \forall x \in R \)
(b) for \( k0 \) the number zero lies between the zeros of the polynomial
(c) \( f(x)=0 \) has two distinct solutions in \( (0,1) \) for \( k \in(1 / 4 \), \( 4 / 7) \)
(d) Minimum value of \( f(x) \forall k \in R \) is \( k(1+12 k) \)
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