Find all zeros of f(x)=x^4-3x^3+6x^2+2x-60 given that 1+3i is a zero of f(x)

The roots of f(x) are: -2, 3, (1+3i) and (1-3i)

Step-by-step explanation:

We are given an expression:

(1+3i) is a root of f(x)

We have to find the remaining roots of f(x).

Since, (1+3i) is a root of f(x),

is a factor of given expression.

Now, we check if (1 - 3i) is a root of given function.

Thus, (1-3i) is also a root of given function.

Since, (1-3i) is a root of f(x),

is a factor of given expression.

Thus, we can write:

Dividing f(x) by above expression:

To find the root, we equate it to zero:

Thus, the roots of f(x) are: -2, 3, (1+3i) and (1-3i)

hello from mrbilldoesmath!

answer:

25x^2 + 90x + 84

discussion:

mn(x) = m(n(x)) = m( 5x + 9) =

(5x + 9)^2 + 3 =>

25x^2 + 90x + 9^2 + 3 =

25x^2 + 90x + 84                 (as 9^2 = 9*9 = 81)

which is the second choice

regards,  

mrb

p.s.   i'll be on vacation from friday, dec 22 to jan 2, 2019. have a great new year!

chiken

step-by-step explanation: