A polynomial f𝑓 with rational coefficients has 5−√35−3 as a root. Find another root of f.
Question
A polynomial f𝑓 with rational coefficients has 5−√35−3 as a root. Find another root of f.
Solution
The roots of a polynomial with rational coefficients always come in conjugate pairs if they are complex or irrational. The conjugate of a number is formed by changing the sign of its imaginary (or irrational) part.
Given that one root is 5 - √3 - √5, the conjugate of this root would be 5 + √3 + √5.
So, 5 + √3 + √5 is another root of the polynomial f.
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