Question

Patricia is studying a polynomial function f(x). Three given roots of f(x) are -11-√2i , 3 + 4i, and 10. Patricia concludes that f(x) must be a polynomial with degree 4. Which statement is true?
A. Patricia is correct because -11+√2i must be a root.
B. Patricia is correct because 3 – 4i must be a root.
C. Patricia is not correct because both 3 – 4i  and -11+√2i  must be roots.
D. Patricia is not correct because both 3 – 4i  and 11+√2i  must be roots

Answer 1

Answer:

D) Patricia is not correct because both 3 – 4i and Negative 11 + StartRoot 2 EndRoot i must be roots.

Step-by-step explanation:

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Answer 2

Patricia is not correct because both $3-4i$ and $11+\sqrt{2} i$  must be roots.

What are polynomial function?

A polynomial function is a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc.

According to questions, Patricia is studying a polynomial function f(x). Three given roots of f(x) are $-11-\sqrt{2} i$ , $3 + 4i,$ and $10$. Patricia concludes that f(x) must be a polynomial with degree $4.$

Since   $-11-\sqrt{2} i$  and  $3 + 4i$ are the roots of $f(x)$ , so   $3-4i$ and $11+\sqrt{2} i$ must be its roots.

Hence, Option(D) is correct.

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