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, we need to consider the properties of the given root 3−7–√.
First, let's simplify the expression 3−7–√ :
3−7–√ = 3 - 7 - √(-1) (Since √(-1) is equivalent to i)
= 3 - 7 - i
= -4 - i
Therefore, the given root is -4 - i.
To find another root, we know that complex roots occur in conjugate pairs. This means that if -4 - i is a root, its conjugate -4 + i will also be a root.
Hence, -4 + i is another root of the polynomial.