Question

Please help / Fan and Medal.
I'm dying here ):
Susi and Janet have been solving systems of equations with one polynomial function of degree two or higher and one linear function. Janet says there must always be one solutions, and Susi says there will always be two solutions. Using complete sentences, explain how Susi can be correct, how Janet can be correct, and how they both can be wrong.

Answer 1

@myininaya

Answer 2

so image we have the function f(x)=ax^2+bx+c

Answer 3

you know the discriminant is b^2-4ac
when the discriminant is 0 how many real solutions do we have?
when the discriminant is positive how many real solutions do we have?
when the discriminant is negative how many real solutions do we have?

Answer 4

Could you right out the equation, I forgot what it looked like and typing the question confuses me

Answer 5

what equation are you asking about?

Answer 6

I was going to first have you consider functions in the form y=ax^2+bx+c
and then use that same knowledge to provide a conjecture about functions in the form
y=ax^3+bx^2+cx+d.
Then we could say something about polynomial functions of degree n.

Answer 7

for example,
for the 2nd degree polynomial
pretend we have
f(x)=x^2 <--how many real solutions does this one have?
f(x)=x^2+1 <--how many real solutions does this one have?
f(x)=x^2-1 <--how many real solutions does this one have?

Answer 8

the first one, zero. the second, one. and the third one, two. am I correct? @myininaya

Answer 9

yes
so what does that mean f(x)=ax^2+bx+c can have at most 2 real solutions since we seen it could have either 0, 1 , or 2 solutions.

Answer 10

so if a f(x)=ax^2+bx+c can have at most 2 real solutions
then f(x)=ax^3+bx^2+cx+d can have at most what real solutions?

Answer 11

two solutions?

Answer 12

THREE! sorry

Answer 13

well a second degree polynomial has a most 2 real solutions
so third degree polynomial would have most how many real solutions?

Answer 14

yes! :)

Answer 15

at most means it doesn't have to be exactly 3
it could be 2
1 or even 0

Answer 16

So how exactly could I answer this question?
Im not exactly good at this ):
I know that if the function touched the line one time, theres one solution. I know that if It hits it twice, theres two solutions. if the parabola doesn't touch the line at all, there is no solution... but how exactly can I answer this question? help?

Answer 17

@myininaya

Answer 18

that sounds like a good start for the 2nd degree poly

you can expand what you said for a 3rd degree on (except don't call it a parabola because it isn't )

Answer 19

I would also provide at least the parabola examples too.