Question

Question 5
answer fastly and correctly

Answer 1

Given f(x) = x^4 - 6x^3 + 16x^2 - 25x + 10.

Given g(x) = x^2 - 2x + k.

Now,

x^2 - 2x + k) x^4 - 6x^3 + 16x^2 - 25x + 10 ( x^2 - 4x + (8 - k)

                    x^4 - 2x^3 + kx^2

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

                         -4x^3 + (16 - k)x^2 - 25x  

                        -4x^3   +  8x^2       - 4kx

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

                                   (8 - k)x^2 + (-25 + 4k)x + 10

                                   (8 - k)x^2 - 2(8 - k)x + k(8 - k)

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

                                               (-25 + 4k + 16 - 2k)x + 10 - 8k + k^2

Now,

(i) -25 + 4k + 16 - 2k = 1

=> -9 + 2k = 1

= > 2k = 10

= > k = 5.

(ii)

= > 10 - 8k + k^2 = a

= > 10 - 8(5) + (5)^2 = a

= > 10 - 40 + 25 = a

= > -30 + 25 = a

= > a = -5.

Hope this helps!

Answer 2

This is the answers for this