Let P ( x ) = x 2 + b x + c , where b and c are integer. If P ( x ) is a factor of both x 4 + 6 x 2 + 25 and 3 x 4 + 4 x 2 + 28 x + 5 , find the value of P ( 1 ) .

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Since P ( x ) divides into both of them Hence P ( x ) also divides ​ ( 3 x 4 + 4 x 2 + 28 x + 5 ) − 3 ( x 4 + 6 x 2 + 25 ) ​ = − 14 x 2 + 28 x − 70 = − 14 ( x 2 − 2 x + 5 ) ​ Which is a quadratic, Hence P ( x ) = x 2 − 2 x + 5 ∴ P ( 1 ) = 4

Mathematics - Quadratic Equation Question with Solution | TestHub

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