What causes an equation to have a solution that has complex numbers?

Question

it los the last question for my online homework and I don’t know how to answer it

Answer 1

I believe you are speaking of the general equation:

y = ax²+bx+c

which has two solutions for y=0,

or you are speaking of the equation:

ax²+bx+c=0

(since this is Algegra 2)

which has two solutions (this is the same as above with y=0)

given by:

x = (-b±√(b²-4ac))/2a

when b²-4ac < 0

you get complex roots

that is, when the quantity under the square root sign is negative, then the answer is complex (the square root of a negative number is an imaginary number, thus, the solution will be two complex numbers that are the complex conjugates of each other.

when b²-4ac > 0

you get real roots

that is, when the quantity under the square root sign is positive, then the solution yields two real numbers for the roots.