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If a polynomial function f(x) has roots 3 and square root of 7, what must also be a root of f(x)?
Solution:
Given, a polynomial function f(x) has root 3 and √7.
Here, 3 is a real number.
√7 is an irrational number.
The root of the function always occurs in conjugate pairs.
Conjugate pair is a root which has two forms, one positive and one negative.
Example: a+√b and a-√b
For the given function f(x), √7 should be in conjugate pairs.
Other root of f(x) should be -√7
Therefore, the other root must be negative of root 7.
If a polynomial function f(x) has roots 3 and square root of 7, what must also be a root of f(x)?
Summary:
If a polynomial function f(x) has roots 3 and square root of 7, the other root must be -√7.
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