Question

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Answer 1

Given x^2 + 2x + 5 is a factor of x^4 + Px^2 + Q


x^2 + 2x + 5) x^4 + px^2 + q

                      x^4  + 2x^3 + 5x^2

                      ----------------------------

                             -2x^3 + (p - 5)x^2 + q

                             -2x^3 - 4x^2  - 10x

                      ---------------------------------------
    
                                        (p - 1)x^2 + 10x + q

                                        (p - 1)x^2 + (2p - 2)x + (5p - 5)

                      --------------------------------------------------------------

                                                        (10 - 2p + 2)x + (q-5p + 5)



(i)

= > 10 - 2p + 2 = 0

= > 12 - 2p = 0

= > p = 6.



(ii) q - 5p + 5 = 0

= > q - 5(6) + 5 = 0

= > q - 30 + 5 = 0

= > q - 25 = 0

= > q = 25.


Now,

p + q = 25 + 6

          = 31.


Therefore, the answer is Option(3).


Hope this helps!

Answer 2

Hey!!!

Refer to the attachment

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Hope it will helps you:-)