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Let a and b be two distinct roots of a p...

Let a and b be two distinct roots of a polynomial equation f(x) =0 Then there exist at least one root lying between a and b of the polynomial equation

A

f(x)

B

f'(x)

C

f''(x)

D

none of these

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The correct Answer is:
B
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OBJECTIVE RD SHARMA-MEAN VALUE THEOREMS-Exercise
  1. Let a and b be two distinct roots of a polynomial equation f(x) =0 The...

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  2. If 2a+3b+6c=0, then prove that at least one root of the equation a x^2...

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  3. Let f(x)a n dg(x) be two functions which are defined and differentiabl...

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  4. Let f be differentiable for all x , If f(1)=-2a n df^(prime)(x)geq2 fo...

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  5. If the function f(x)=x^3-6x^2+a x+b defined on [1,3] satisfies Rolles ...

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  6. Let (a0)/(n+1)+(a1)/n+(a2)/(n-1)++(a(n-1))/2+an=0. Show that there e...

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  7. The number of values of k for which the equation x^3-3x+k=0 has two di...

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  8. Let f(x)=(x-4)(x-5)(x-6)(x-7) then. (A)fprime(x)=0 has four roots (B)T...

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  9. Let fa n dg be differentiable on [0,1] such that f(0)=2,g(0),f(1)=6a n...

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  10. If the polynomial equation an x^n + a(n-1) x^(n-1) + a(n-2) x^(n-2) + ...

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  11. The equation x log x = 3-x has, in the interval (1,3) :

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  12. If f(x) and g(x) ar edifferentiable function for 0lex le1 such that f(...

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  13. If alpha beta( alpha lt beta) are two distinct roots of the equation. ...

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  14. If (x) is a function given by f(x) = |{:(sinx , sin a, sin b),(cosx,c...

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  15. The value of c in Largrange's theorem for the function f(x)= log(e) s...

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  16. n is a positive integer. If the value of c presecribed in Rolle's th...

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  17. The distance travelled by a particle upto tiem x is given by f(x)=x^(...

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  18. The number of real root of the equation e^(x-1)+x-2=0, is

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  19. If the polynomial equation an x^n + a(n-1) x^(n-1) + a(n-2) x^(n-2) + ...

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  20. If 4a+2b+c=0 , then the equation 3ax^(2)+2bx+c=0 has at least one rea...

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