Question

Determine between which consecutive integers the real zeros of F(x)=2x^2-5x+1 are located.
a. between 0&1 and 1&2
c. between 0&1 and 2&3
b. between -1&0 and 2&3
d. between 1&2 and 2&3

Answer 1

@Georgiapeach0106

Answer 2

hello

Answer 3

@Georgiapeach0106 message me.

Answer 4

Welcome to OpenStudy!! Are you Devauhgn or Devaughn? Your bio says Devauhgn.

First: are you familiar with "synthetic division?"
Second: Do you have a graphing calculator?

Answer 5

1: yes
2:no

Answer 6

oh and yes devaughn.

Answer 7

Nice having you here, Devaughn!

Double check that your function is f(x) = x^2 -5x + 1.
If that is correct, then you might want to test possible roots such as {-2,-1,0,1, 2} using synthetic division. Suppose (just suppose) that you get a - remainder for x=-2 and a positive remainder for x=-1. That would tell you that the graph crosses the x-axis between x=-2 and x=-1. Have you heard this kind of reasoning discussed before?

Answer 8

no.

Answer 9

Here's another way to look at this matter, Devaughn: If you use -2 as the divisor in synthetic division, the "remainder" is also the value of the function at x=-2. Did you know that? The idea is that if the function is + at x=-2 and neg at x=-1, the graph HAS TO cross the x-axis between -2 and -1.

Answer 10

OK. Please try this: Either use the possible root 0 (zero) in synthetic div to determine what the value of the function is at x=0, or just take the function and plug in x=0. Your choice. At x=0, the y value is ... ?

Answer 11

oh. and 1

Answer 12

Good!
Now, do the same thing for x=1. The value of y at x=1 is ... ?

Answer 13

0?

Answer 14

No, sorry. Try finding f(1). Substitute 1 for x in your function. y = ? at x=1

Answer 15

Or use synth div again.

Answer 16

-2

Answer 17

Perfect.

Answer 18

so, you see, Devaughn, the function changes sign as you go from 0 to 1. Does this agree with your calculations or not?

Answer 19

yes

Answer 20

Just a reminder: If the function changes sign between 0 and 1, then we have a real root between 0 and 1. We don't know its value, but we do know we have it.

Now, please use x=2 as divisor in synth. div. If x=2, y = ??

Answer 21

At x=1, y=-2. At x=2, y = ?

Answer 22

oh i got it now. thank you.

Answer 23

I'm so glad. I hope you'll come back to OpenStudy again and again.

Note that there is no change of sign as you move from x=1 to 2...therefore there is NO root between 1 and 2. There is a change of sign as you move from x=2 to x=3, so yes, you have a root between 2 and 3.

Answer 24

Take care, devaughn. See you again here on OS!

Answer 25

i did callme