# By using Rolle's theorem it is impossible for the function f(x)=(x^5) + x - 12 to have two real roots. This is because if f(x) has two real roots then by Rolle's theorem, f '(x) must be _________ at certain value of x between these two roots, but f '(x)  is always positive.

Question
63 views

By using Rolle's theorem it is impossible for the function f(x)=(x^5) + x - 12 to have two real roots.

This is because if f(x) has two real roots then by Rolle's theorem, f '(x) must be _________ at certain value of x between these two roots, but f '(x)  is always positive.

check_circle

Step 1

The complete sentence should be as shown below:

This is because if f(x) has two real roots then by Rolle's theorem, f '(x) must be zero at certain value of x between these two roots, but f '(x)  is always positive.

Step 2

Let's assume f(x) = x5 + x - 12 has two real roots, say a and b and without loss of generality, let's further assume a < b

Then f(a) = f(b) = 0

As per Rolle'...

### Want to see the full answer?

See Solution

#### 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