Question

what does the graph for ..... look like?
-cubic with one real solution and two complex solutions look like?
-cubic with no real solutions?
-quartic with no real solutions?
-a quadratic with one real solution and one complex solution?
-a quartic with two real solutions and two complex solutions?
-a quadratic with no real solutions?
-a quartic with no real solutions?
-a cubic with 3 real solutions, but one is a double root?
-a quartic with for real roots, but both are double roots?

Answer 1

I'm assuming you mean when the polynomial is set equal to 0.

-cubic with one real solution crosses the x axis exactly one time
-cubic with no real solutions doesn't exist because complex solutions come in conjugate pairs and the degree is odd.
-quartic with no real is a parabola either completely above or completely below the x axis
-quadratic 1 real 1 complex does not exist since complex solutions come in conjugate pairs.
-quartic 2 real 2 complex: parabola crossing the x axis twice
-quadratic no real solutions: parabola either completely above or completely below x-axis
-quartic no real solutions: I think you asked this twice
-cubic with 3 real roots one a double root. Looks like a standard cubic but one of the "humps" just exactly touches the xaxis and then curves away.
-quartic 4 real roots 2 double: two parabolas merged together with the bottoms or tops both just touching the xaxis and then curving away.

Note: quartic doesn't look exactly like a parabola it is more like 2 parabolas with a bump at the bottom that curves in the opposite direction of the rest of the parabola.

I can give you a picture of any of these if you'd like.

Answer 2

ok and can you give me a picture of all of them?

Answer 3

I can give you a picture of a quartic quadratic and cubic, and then you should be able to figure out what they look like from my descriptions hopefully.

Answer 4

okay

Answer 5

what about a quartic with no real solutions?

Answer 6

The three shapes are in a word document with one of the specific cases for each. Look through them and then look at my first post. Quartic with no real solutions has quartic shape but is either completely above or below the xaxis

Answer 7

each of the shapes can be flipped upside down by changing the sign of the term with highest degree. In the word file they are all positive

Answer 8

thanks :)

Answer 9

you're welcome :)

Answer 10

but i couldnt tell the difference between the quartic and the quadratic

Answer 11

the quartic is like three pieces of parabolas put together, do you see the bump in the middle? quadratic is a single parabola

Answer 12

ok thanks