Question

What can we afirm about the roots of 2x³ - x² - 2x + 1 = 0 ?

a) only one of them is irrational
b) they belong to [-1,1]
c) two of them are negative
d) none of them is real

Can someone help me? I divided it by x - 1 and got x = -1 and x = 1/2. Is it right to say they belong to [-1,1]? Because option 'a' also seems right. Help!

Answer 1

2x³ - x² - 2x + 1 = 0 has 3 roots x=1 x=-1 x=1/2

Answer 2

Still, both a and b seem right.

Answer 3

When x=-1 y=0 , it cant be b)

Answer 4

a

Answer 5

Yep, it can be b as well. why do you think its a?

Answer 6

When x=-1 y=0 , it cant be b

Answer 7

For [-1,1]

Answer 8

I know that. Why did you post 'a'?

Answer 9

b) they belong to [-1,1]

No roots for this polynomial are irrational.

Do you know the Rational Roots Theorem, Synthetic Division?

I don't know the divisor you used for your division or the dividend but if you provide that information or perhaps use the "Draw" button to write your division, I will try to help you.

Answer 10

After finding 2x² + x - 1 I did this:
x = - 1 + sqrt9 / 4
x = -1 - sqrt9 /4
Then I got x = -1 and x = 1/2

Answer 11

1/2 is irrational, isn't it?

Answer 12

oops haha

Answer 13

1/2 is rational. A rational number is one that can be written as the ratio of 2 integers. The first 5 letters of ratio nal are a reminder.

Answer 14

Yep, sorry.

Answer 15

What did you divide by to get 2x² + x - 1? I'm trying to tune in to your thinking. I just saw this thread.

Answer 16

I divided 2x³ - x² - 2x + 1 by x - 1

Answer 17

remainder's 0 so I guess it's right

Answer 18

Okay, I got the same quotient. 2x^2 + x -1 should factor.

Answer 19

(2x - 1) (x + 1) = 0

2x - 1 = 0 or x + 1 =0

x = 1/2 or x = -1

Answer 20

Thanks. I can see it clearly now, it's b indeed.

Answer 21

You understand the [-1,1] notation. Yes?

Answer 22

Yep. Thx a lot

Answer 23

Great.