Question

Which two values of x are roots of the polynomial x^2 + 5x + 7?

a) x = -5 + 2√3
b) x = 5 - √17
c) x = 5
d) x = 5.13

Answer 1

The roots of the polynomial x^2 + 5x + 7 are not among the provided options since the discriminant is negative, indicating that there are no real roots.

Step-by-step explanation:

The given polynomial is x^2 + 5x + 7. To find its roots, we could apply the quadratic formula x = −b ± √(b^2 − 4ac) / (2a), where a = 1, b = 5, and c = 7 in this case. However, looking at the provided solutions, none of them seem to be derived from these coefficients. In fact, the given solutions belong to different quadratic equations, not the one stated in the question (x^2 + 5x + 7).

Without proper roots given for the polynomial in question, we cannot affirm that any of the presented options (a through d) are correct. To accurately determine the roots for the original equation, we would need to compute using the actual coefficients a = 1, b = 5, and c = 7:

−5 ± √(5^2 − 4 × 1 × 7) / (2 × 1)

As the discriminant (b^2 - 4ac) is negative, this polynomial does not have real roots, hence none of the options match the solution to the original polynomial.