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p(x) = x^2+bx +c where band c are integers if p(x) is a factor of both x^4 +6x^2+25 and 3 x^4 +4x^2+28x +5 then find p(1)


 p(x) = x^2+bx +c where band c are integers if p(x) is a factor of both x^4 +6x^2+25 and 3 x^4 +4x^2+28x +5 then find p(1)


 


Grade:12

1 Answers

shaswat roy
19 Points
9 years ago

let q(x) be  x^4 + 6x^2 +25    and  let r(x)  be  3x^4 + 4x^2 + 28x +5

since p(x) is a factor of q(x) naturally it will also be a factor of 3q(x). Also, by basic mathematics we can show that p(x) is a factor of  "3q(x) - r(x)"

3q(x) - r(x) = 14x^2 - 28x + 70 = 14(x^2 - 2x + 5)

i think you will now be able to solve the problem completely.

 

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