let f(x) = x2 + bx + c where b , c are integers . if f(x) is a factor of both x4 + 6x2 +25 and 3x4 + 4x2 + 28x + 5 , then the value of f(1) is :

(a) 1

(b) 2

(c) 3

(d) none of these

Correct option (d)f(x) is common factor of expressions 3x4+ 4x2+ 28x + 5 and x4+ 6x2+25So, f(x) is the HCF of the two expressionsx4+ 6x2+2533x4+ 4x2+ 28x + 5  3x4+18x2+ 7514x2+28x75+5R(x)=14(x22x+5)So the HCF is (x22x+5)Comparing with expression x2+bx+cb=2, c=5So the required expression f(x)=x22x+5=>f(1)=122×1+5=4

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