Question

I am not 100% sure I got these right could you check please? thank you!

Answer 1

they all look okay to me. I dont know if they are right or not.

Answer 2

they were all greater than zero in the discriminant so I thought that would mean 2 solutions, but all of the answer choices have me confused and second guessing

Answer 3

what do yall think?

Answer 4

They are not all correct. How did you determine your answer choices?

Answer 5

I put them into quadratic formula form and then solved the discriminant. In each case they were all greater than zero, meaning two solutions (I thought)

Answer 6

Well, yes, it does mean that, but it doesn't tell you that all of the solutions will be positive ones.

For example, how about \[x^2+2x-3=0\]
What is discriminant?

Answer 7

and what are solutions?

Answer 8

the discriminant is sqrt 4-4(1)(-3)= sqrt 16 = 4?

Answer 9

no, no square root, or the discriminant would always be positive.

discriminant for a quadratic is just \(b^2 - 4ac\)

Answer 10

so it would be 16 then?

Answer 11

so discriminant for this equation is 16. But what are the solutions?

Hint: \[x^2+2x-3 = (x-1)(x+3)\]

Answer 12

1, -3 ?

wait is this wanting me to factor not do the discriminant?

Answer 13

cuz im awesome at factoring! lol

Answer 14

No, I'm trying to enlighten you about the meaning of various values of the discriminant.

So here we have a quadratic with a positive discriminant, but not all of the solutions are positive. That means that we cannot assume that a positive discriminant --> all solutions positive.

Answer 15

oh ok, I see what you are saying! I cant just assume that because the discriminant came out to be positive, that all solution for the equation are positive

Answer 16

What we can determine from the discriminant is this:

\[\Delta = b^2 - 4ac\]\[\Delta > 0 \rightarrow \text{2 real solutions}\]\[\Delta = 0\rightarrow \text{1 real solution with multiplicity 2}\]\[\Delta < 0 \rightarrow\text{2 complex solutions in conjugate form, }a\pm bi\]

Answer 17

multiplicity 2 means that there's a solution that happens twice. For example:

\[y = x^2\]has \[\Delta = 0^2-4(1)(0) = 0\]and the solutions are obviously \[x=0,x=0\]

Answer 18

? new answers i got?

Answer 19

So to do this problem, you can use the discriminant to make the first classification (real solutions, single real solution, complex solutions) but you'll need to factor or otherwise solve to do the second part of characterizing those solutions.

Answer 20

Your answer for #38 is still incorrect. @Bookworm14

Answer 21

Do you still need help?

Answer 22

idk where i went wrong

Answer 23

What do you get for solutions for problem 38?