defence exam Army Havildar SAC Mock Test Series 2025 Mathematics Quadratic Equations

Let f(x) = x2 - bx + c, b is an odd positive integer. If f(x) = 0 has to prime numbers as roots and b + c = 35, then the global minimum value of f(x) is 

1
\(- \frac {183} 4\)
2
\(\frac {173} {16}\)
3
\(- \frac {81} 4\)
4
\(\frac {17} 2\)
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