# Find a fourth-degree polynomial function f(x) with realcoeffi cients that has -1, 1, and i as zeros and such thatf(3) = 160.

Question
30 views

Find a fourth-degree polynomial function f(x) with real
coeffi cients that has -1, 1, and i as zeros and such that
f(3) = 160.

check_circle

Step 1

Since two zeros are -1 and 1, so two factors are (x+1) and (x-1), The complex zeros occur in conjugate pairs,so if i is its zero ,then -i is also its zero

Therefore, two other factors are (x+i) and (x-i), that is (x+i) (x-i)=(x^2+1)  is also its factor .

So, we assume the polymial as f(x) =a(x+1)(x-1)(x^2+1) as shown on board.

Step 2

Now, we use the condition f(3)=160 and find the value of a

Substitute...

### Want to see the full answer?

See Solution

#### Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

### Algebra 