Question

Need help with this ​

Answer 1

`x^4-20x^3 +175x^2 -750x+1250`

Explanation:

By the conjugate root theorem, 5+5i is also a root.

`f(x)=a(x-5)^2 (x-5-5i)(x-5+5i) \\ \\ </p><p>= a(x^2 - 10x+25)((x-5)^2 - (5i)^2) \\ \\ </p><p>= a(x^2 - 10x+25)(x^2 - 10x+25+25) \\ \\ </p><p>= a(x^2-10x+25)(x^2-10x+50) \\ \\ </p><p>= a(x^4- 10x^3 + 50x^2 - 10x^3 + 100x^2 - 500x + 25x^2 - 250x+1250) \\ \\ </p><p>= a(x^4-20x^3 +175x^2 -750x+1250) \\ \\`