Question

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

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0.

1.

f(a).

-1.

f(b).


This result is called the

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Polynomial

Intermediate Value

Factor

Rational Zero


Theorem.

Answer 1

Answer:

this is intermediate value theorem

Step-by-step explanation:

Explanation:-

• The curve is the function y = f(x)
• which is continuous function on the interval [a, b]
• and 'd' is a number between f(a) and f(b) then

• there must be at-least one value c with in [a ,b] such that f(c)=d

Example:-

       let assume the polynomial is $x^{5}-2x^3-2=0$  and given interval is

[0,2]

    solution:-  At x=0

                       f(x) = $x^{5}-2x^3-2$

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

so f(0) is negative.

                   At x=2

                   f(x) =$x^{5}-2x^3-2$

                   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