Question
Asked Dec 10, 2019
12 views
Show Hhat the equathon
3
X°+2x -23D0
has exacthy
one realroot.
lyt
help_outline

Image Transcriptionclose

Show Hhat the equathon 3 X°+2x -23D0 has exacthy one realroot. lyt

fullscreen
check_circle

Expert Answer

Step 1

Given function is

help_outline

Image Transcriptionclose

f(x) = x' + 2x – 2

fullscreen
Step 2

For the positive real root of the given function, look the number of sign changes of polynomial for +x which is

help_outline

Image Transcriptionclose

f(+x)= x +2x - 2 Here there is one changes from + 2x to – 2. So, there is only one positive real root.

fullscreen
Step 3

For the negative real root of the given function, look the numbe...

help_outline

Image Transcriptionclose

f(-x)= 4(-x)³ + 2(-x)-2 f(-x)= -4x - 2x- 2 Here there is no sign change. So, there is no negative real root.

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus