# Maths

posted by .

The function f(x)=x^4−15(x^3)+81(x^2)−201x+182 has four complex roots, one of which is 3−2i. What is the sum of all real and imaginary coefficients of these roots?

Details and assumptions
i is the imaginary unit, where i2=−1.

• Maths -

one other complex root must be 3+2i
So, (x-(3-2i))(x-(3+2i)) are factors of f(x)

That is, (x-3)^2+4 = (x^2-6x+13) divides f(x)

f(x) = (x^2-6x+13)(x^2-9x+14)
= (x^2-6x+13)(x-2)(x-7)

So, the roots are
2,7,3-2i,3+2i

## Similar Questions

1. ### Precalculus

"Show that x^6 - 7x^3 - 8 = 0 has a quadratic form. Then find the two real roots and the four imaginary roots of this equation." I used synthetic division to get the real roots 2 and -1, but I can't figure out how to get the imaginary …
2. ### biology

Given the part of the molecule shown below, can the underlined atom participate in a hydrogen bond with an approriate bonding partner?
3. ### Algebra

The function f(x)=x^4−10x^3+40x^2−80x+64 has four complex roots, one of which is 2−2i. What is the sum of all real and imaginary coefficients of these roots?
4. ### Product of Roots of Sums of Products of Difference

What is the product of all roots to the equation ++(x−1)(x−2)(x−3)+(x−2)(x−3)(x−4)(x−3)(x−4)(x−5)+(x−4)(x−5)(x−6)(x−5)(x−6)(x−7)+(x−6)(x−7)(x−8)=0?
5. ### Product of Roots of Sums of Products of Difference

What is the product of all roots to the equation ++(x−1)(x−2)(x−3)+(x−2)(x−3)(x−4)(x−3)(x−4)(x−5)+(x−4)(x−5)(x−6)(x−5)(x−6)(x−7)+(x−6)(x−7)(x−8)=0?
6. ### maths

Suppose z=a+bi, where a and b are integers and i is the imaginary unit. We are given that |1+iz|=|1−iz| and |z−(13+15i)|<17. Find the largest possible value of a+b. Details and assumptions i is the imaginary unit, where …
7. ### Maths

Suppose z=a+bi, where a and b are integers and i is the imaginary unit. We are given that |1+iz|=|1−iz| and |z−(13+15i)|<17. Find the largest possible value of a+b. i is the imaginary unit, where i^2=−1.