If 2 + 43 is a polynomial root, name another root of the polynomial, and explain how you know it must also be a root.
To find another root of the polynomial, we need to understand the concept of polynomial roots. A polynomial root is a value of the variable that makes the polynomial equation equal to zero.
We know that 2 + 43 is a root of the polynomial, which means that when we substitute 2 + 43 into the polynomial equation, it will equal zero. Let's call the polynomial equation P(x).
Therefore, we know that P(2 + 43) = 0.
Now, when we want to find another root of the polynomial, we need to consider the concept of conjugate roots. For any polynomial with real coefficients, complex roots (numbers with an imaginary component) occur in conjugate pairs.
Since 2 + 43 is a real root, we can deduce that its conjugate would also be a root of the polynomial. The conjugate of any real number is itself.
Therefore, the other root of the polynomial is 2 + 43 (the same as the given root), and we know it must also be a root because it is the conjugate of the given root.