F f is a polynomial function and f(a) and f(b) have opposite signs, then there must be at least one value of c between a and b for which f(c)equals

▼

0.

1.

f(a).

-1.

f(b).

This result is called the

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Polynomial

Intermediate Value

Factor

Rational Zero

Theorem.

this is intermediate value theorem

Step-by-step explanation:

Explanation:-

Example:-

       let assume the polynomial is  and given interval is

[0,2]

    solution:-  At x=0

                       f(x) =

                       f(0) = 0-0-2=-2<0

so f(0) is negative.

                   At x=2

                   f(x) =

                   f(2) = 32-16-2=14 >0

so f(2) is positive.

there f(a) is negative and f(b) is positive the there must be at-least one value of 'c' between 'a' and 'b'

       let assume c=1 between [0,2]

             f(1) = 1-2-2 = -3

answer: 2 and 1

step-by-step explanation: got this question

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step-by-step explanation: