Question

Find the roots of the polynomial f(x) = x² + 2x + 10.

a) x = -1 + 3i
b) x = -1 - 3i
c) x = -1 + isqrt(3)
d) x = -1 - isqrt(3)

Answer 1

The roots of the polynomial f(x) = x² + 2x + 10 can be found using the quadratic formula. The roots are -1 + 3i and -1 - 3i.

Step-by-step explanation:

The roots of the polynomial f(x) = x² + 2x + 10 can be found using the quadratic formula.

In this case, the coefficients are a = 1, b = 2, and c = 10. The formula is:

x = (-b ± √(b² - 4ac)) / (2a)

Substituting the values, we have:

x = (-2 ± √(2² - 4(1)(10))) / (2(1))

Simplifying further:

x = (-2 ± √(-36)) / 2

The square root of a negative number is an imaginary number, so the roots of the polynomial are:

x = -1 + 3i and x = -1 - 3i