Answer :
Final answer:
To find f(7i) for the function f(x) = 2x² + 62, apply the Remainder Theorem using synthetic division with 'k' = 7i. The result will be a complex number, as 'k' is a complex number.
Explanation:
The function given is a quadratic complex polynomial, and the value you're asked to find, k, is a complex number (7i). The Remainder Theorem states that the remainder of the division of a polynomial f(x) by a binomial x - k is equal to f(k).
For f(x) = 2x² + 62 and k = 7i, we need to perform synthetic division:
- Write down the coefficients of the polynomial, (2 and 62), and also write down the value of 'k' (7i).
- Beneath the first coefficient, write a zero. This begins the second row of the synthetic division.
- Drop down the first coefficient (2) to the start of the second row.
- Multiply the value just written by 'k', and write this beneath the next coefficient in the top row.
- Add these two numbers and write result under the line. This number is the next number in the second row.
- Continue this process until the end.
At the end of the division, the number on the bottom right is the value of f(k), which in this case, will be a complex number due to the complex 'k' value used.
Learn more about Remainder Theorem here:
https://brainly.com/question/35460223
#SPJ11
