Question

question 8 of 10
the discriminant of a quadratic equation is negative. one solution is 6 + 2i. what is the other solution?

a. 6 - 2i

b. 2 - 6i

c. 2 + 6i

d. -6 + 2i

Explanation:

Step1: Recall conjugate root theorem

For a quadratic equation with real coefficients, if the discriminant is negative, the roots are complex conjugates. A complex number \(a + bi\) has a conjugate \(a - bi\).

Step2: Apply to given solution

Given one solution is \(6 + 2i\), its complex conjugate (the other root) should be \(6 - 2i\) as we change the sign of the imaginary part.

Answer:

A. \(6 - 2i\)