Question

the function below crosses the x-axis twice
true or false
2x^2-3x+1

Answer 1

Under what condition will a quadratic cross the x-axis twice? What do you know about the roots, if it crosses twice?

Answer 2

its positive huh

Answer 3

What's positive?

Answer 4

(You might be right - I just need to see exactly what you mean by that.)

Answer 5

if it crosses twice its positive

Answer 6

OK, "its" is very vague here, lol. I asked you: what does the fact that a quadratic crosses the x-axis twice tell you about the roots of the quadratic?

Answer 7

There are 3 possibilities for the roots of a quadratic:

2 real roots
1 repeated real root (something like \((x-3)^2=0\) means 3 is a repeated root
or no real roots (2 imaginary roots)

Each of those situations has a certain "look" to the graph, in terms of where/if/how many times the function crosses the x-axis. I'm asking you, if you understand that connection.

Answer 8

And there is SOMETHING that tells you WHICH of those 3 situations you are in. Do you know what that something is?

Answer 9

ohhhhh its gonna be false cuz theres a negative

Answer 10

I'm still not sure what you mean. What's a negative??

Answer 11

becuse if it negative it cross the x-axis zero times

Answer 12

Remember the discussion yesterday about crossing/touching and the discriminant? This is closely related to that.

Answer 13

IF WHAT'S NEGATIVE?

Answer 14

http://openstudy.com/study#/updates/52153cdae4b0450ed75e459c

If discr>0, there are 2 DISTINCT real roots - what does that mean in terms of it's behavior crossing/touching the axis?

If discr=0, there is ONE REPEATED real root - what does that mean in terms of it's behavior crossing/touching the axis?

if discr<0, there are NO REAL roots (only complex roots) - what does that mean in terms of it's behavior crossing/touching the axis?

Answer 15

@romanortiz65 what's the value of the discriminant for this function?

Answer 16

-5 or +1

Answer 17

There can only be on discriminant. How are you getting 2 values? Show me your work.

Answer 18

*one

Answer 19

1

Answer 20

Right! So how many real roots are there?

Answer 21

two bu what i think the formula is b^2-4ac

Answer 22

Exactly - discrim=(-3)^2-4(2)(1)=9-8=1>0

That means 2 real roots. And that means it crosses the x-axis how many times?