Question

Asked Apr 26, 2019

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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.

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 prove this by contradiction.

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'...

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