when you include complex numbers, does every quadratic equation have 2 solutions?

Answer 1

Yes.

if you use the quadratic equation,
for
ax^2 + bx + c = 0
then,
x = ( -b +/- sqrt(b^2-4*a*c) ) / 2a

There are clearly always 2 answers because for one root you take the "+" and one root you take the "-". Just, sometimes, when the discriminant (b^2 - 4ac) < 0, you have complex roots

Note that for quadratic equations you either have 2 complex roots or no complex roots. It is not possible to have one complex root and one real root (where the graph crosses the x axis. ) When the graph only touches the x axis in one spot, this is a "double real root". It means that BOTH roots are real and they are the same number.... not that there is one real and one complex root.

Answer 2

There are as many roots as the highest power in any equation. That is to say that a second power equation (quadratic) has TWO solutions; a cubic equation has THREE solutions and a fourth power equation has FOUR solutions.
Some solutions may be duplicates (as in a perfect square trinomial), and some may be complex (as when the discriminant is negative for a quadratic), but there are just as many as the highest exponent in the equation.

Answer 3

in the genuine airplane, that's any genuine variety you may think of from unfavourable infinity and helpful infinity then no no longer continuously. If a quadratic does not touch the x-axis it won't have genuine strategies. whether, in the complicated airplane, a quadratic for example 4x^2 + 3x + 2 will continuously have 2 answer. in actuality, any polynomial (like a quadratic) with genuine coefficients would have an identical variety of strategies as its degree over the complicated airplane. So a third degree polynomial would have 3 strategies over the complicated airplane and a 9th degree polynomial would have 9 strategies over the complicated airplane etc...

Answer 4

Yes. When the coefficients are real, the two solutions must be "complex conjugates", but when the coefficients are complex, the roots can be any two complex numbers.

Answer 5

yeah i believe either it will have 2 real root, 1 real 1 img, or both img.

also not that and real number can be written as a complex number.

12 is the same as 12 + (0)i

Answer 6

Yes--If the two roots are equal, we still count
it as 2 roots.