let f(x) = x2+ bx + c where b , c are integers if f(x) is a factor - Maths - Algebraic Expressions and Identities

Question

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

Somnath maths · Accepted Answer

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+ 75−14x2+28x−75+5R(x)=−14(x2−2x+5)So the HCF is (x2−2x+5)Comparing with expression x2+bx+cb=−2, c=5So the required expression f(x)=x2−2x+5=>f(1)=12−2×1+5=4

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

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