Question

A symbolic model for learning is a model that is observed in person. True or False? Question 4030: (Mathematics) If 9i is a root of the polynomial function f(x), which of the following must also be a root of f(x)? a) –9i b) Negative one-ninth c) i d) One-ninth

Answer 1

The correct answer to which other root must exist if 9i is a root of the polynomial function f(x) is -9i, as per the Conjugate Root Theorem.

The correct option is a.

Step-by-step explanation:

If 9i is a root of the polynomial function f(x), then by the Conjugate Root Theorem, the complex conjugate of 9i, which is -9i, must also be a root of f(x). This theorem states that if a polynomial has real coefficients, then the non-real roots of the polynomial occur in conjugate pairs.

This means for every root a + bi, where a and b are real numbers, there is a corresponding root a - bi. Since 9i can be expressed as 0 + 9i, its conjugate is 0 - 9i, which simplifies to -9i.

So the correct answer to the question is option (a) -9i.