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  • Answer please! Let f(x) is a function which is continous and defined in [-4,5] such that f(-4)=2 , f(-2)= -3, f(0)=1 , f(3)= -4 and f(5)= 3 then the equation f(x)= 0 has at least

Let f(x) is a function which is continous and defined in [-4,5] such that f(-4)=2 , f(-2)= -3, f(0)=1 , f(3)= -4 and f(5)= 3 then the equation f(x)= 0 has at least

  • Option 1)

    3 roots 

  • Option 2)

    4roots 

  • Option 3)

    5 roots

  • Option 4)

    6roots

 

Answers (1)

best_answer

As we have learned

Properties of Continuous function -

If  f  is a continuous function defined  on [a,b] such that  f(a)  and  f(b) are of opposite signs then there exists at least one solution of the equation f(x) = 0 in the open interval (a, b)

-

 

 \because f(-4) and f(-2) are of opposite sign so there will be atleast one root in (-4,-2).

Similarly atleast one root in (-2,0) atleast one root in (0,3) and at least one root in (3,5)

so total atleast 4 roots will be there 

 

 

 

 


Option 1)

3 roots 

Option 2)

4roots 

Option 3)

5 roots

Option 4)

6roots

Posted by

Himanshu

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