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

The other solution is 6 - 2i

Whoever wrote this problem made a mistake... the important fact isn't that the discriminant is negative, but that the coefficients are real.

Without that, the other root can be ANY complex number of the form
6+bi
where b is any real number other than 2.

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By the way, I'm assuming your discriminant is the "true" discriminant of
(b/a)^2 - 4(c/a).
If it's the b^2 - 4ac, then your other root could, in fact, be ANY complex number other than 6+2i.

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Needless to say, everything becomes simpler if we correctly assume that the quadratic has real coefficients. Then, and only then, are the other answers correct when stating the answer is 6-2i.

It will be the complex conjugate. In other words, just change the sign in front of the imaginary portion of the complex number.

In general:
a + bi and a - bi

Answer:
6 - 2i

6 - 2i assuming that the coefficients of the quadratic are real

It's 6 - 2i.

All imaginary solutions of quadratic equations come in conjugate pairs, so that means if all the coefficients of the quadratic equation in question are real numbers, its graph doesn't have any real number solutions and won't touch the x-axis in any fashion.

6-2i

6 - 2i
Because complex solutions occur as conjugate pairs