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Dimas [21]
3 years ago
15

Show that the equation x^3+6x-5=0 has a solution between x=0 and x=1

Mathematics
1 answer:
Mnenie [13.5K]3 years ago
6 0

Answer:

Since the value of f(0) is negative and the value of f(1) is positive, then there is at least one value of x between 0 and 1 for which f(x) =0.

Step-by-step explanation:

The equation f(x) given is:

f(x) = x^3+6x-5

For x = 0. the value of the expression is:

f(0) = 0^3+0-5\\f(0) = -5

For x = 1, the value of the expression is:

f(1) = 1^3+6-5\\f(1)=2

Since the value of f(0) is negative and the value of f(1) is positive, then there is at least one value of x between 0 and 1 for which f(x) =0.

In other words, there is at least one solution for the equation between x=0 and x=1.

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