Question

What is the quadratic equation in standard form with rational coefficents that has a root of 5+4i?

Answer 1

x^2 - 10x + 41

Explanation:

since this is a quadratic equation with rational coefficients, the other root must be (5-4i)

now we have (x-(5+4i))(x-(5-4i))

which expands to (x^2) - x(5-4i) -x(5+4i) + (5+4i)(5-4i)

which simplifies to x^2 - 10x + 41

note: (5+4i)(5-4i) = 25 - (-16) = 41