Write the polynomial in simplest form with roots 4, 5i and -5i(multiply it out so no parentheses remain
(x-4)(x+5i)(x-5i)(NOT SURE ABOUT THIS ONE)
(x-4)(x^2-25i^22)
(x-4)(x^2+25)
x^3+25x-4x^2-100
x^3-4x^2+25x-100
Is this correct
that is correct
No, that is not correct. Let's go through the process step by step to find the correct expression.
Given the roots 4, 5i, and -5i, we can write the factors of the polynomial as follows:
1. (x - 4) - This is the factor corresponding to the root 4.
2. (x - 5i) - This is the factor corresponding to the root 5i.
3. (x + 5i) - This is the factor corresponding to the root -5i.
To get the simplified form of the polynomial, we need to multiply these factors together:
(x - 4)(x - 5i)(x + 5i)
Now, let's simplify this expression:
(x - 4)(x^2 - (5i)^2)
Now, let's simplify further:
(x - 4)(x^2 - 25i^2)
Since i^2 is equal to -1, we substitute -1 for i^2:
(x - 4)(x^2 + 25)
Now, let's distribute (multiply) the expression:
x(x^2 + 25) - 4(x^2 + 25)
Simplifying further:
x^3 + 25x - 4x^2 - 100
Reordering the terms:
x^3 - 4x^2 + 25x - 100
So, the correct simplified form of the polynomial is x^3 - 4x^2 + 25x - 100.