If 3−7–√ is a polynomial root, name another root of the polynomial.Explain how you know it must also be a root.
To find another root of the polynomial 3−7–√, we can start by setting the polynomial equal to zero and solving for x:
3−7–√ = 0
Rearranging the equation, we get:
7–√ = 3
Then, subtracting 7 from both sides, we have:
−√ = 3−7 = -4
Now, we can square both sides to eliminate the square root:
(−√)² = (-4)²
Simplifying, we get:
√² = 16
Since the square root and square cancel each other out, we have:
-4 = 16
However, this is not possible as it leads to a contradiction. Therefore, our assumption that 3−7–√ is a root of the polynomial is incorrect.
Hence, we cannot name another root of the polynomial based on this assumption.