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Asked Sep 18, 2019
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53-56 Use the Intermediate Value Theorem to show that
there is a root of the given equation in the specified interval.
53. x4x-3 = 0, (1,2)
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53-56 Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. 53. x4x-3 = 0, (1,2)

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Expert Answer

Step 1

We can prove that f(x) has a root between (a, b) if we can shown that f(a) and f(b) are different in sign.

Step 2

In this case, f(x) = x4 + x – 3 = 0;

(a, b) = (1, 2); Hence, a = 1; b = 2

 

Step 3

f(a) = f(1) = 14 + 1 – 3 = -1;

f(b) = f(2) = ...

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