Let \( f(x)=x^{2}+b x+c \) and \( g(x)=x^{2}+b_{1} x+c_{1} \). Let the real roots of \( f(x)=0 \...

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Let \( f(x)=x^{2}+b x+c \) and \( g(x)=x^{2}+b_{1} x+c_{1} \).
Let the real roots of \( f(x)=0 \) be \( \alpha, \beta \) and real roots of \( g(x)=0 \) be \( \alpha+k, \beta+k \) for same constant \( k \). The least value of \( f(x) \) is \( -\frac{1}{4} \) and least value of \( g(x) \) occurs at \( x=\frac{7}{2} \). The least value of \( g(x) \) is
(a) \( -1 \)
(b) \( -\frac{1}{2} \)
(c) \( -\frac{1}{3} \)
(d) \( -\frac{1}{4} \)
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