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The number of values of k for which the ...

The number of values of `k` for which the equation `x^3-3x+k=0` has two distinct roots lying in the interval `(0,1)` is three (b) two (c) infinitely many (d) zero

A

three

B

two

C

infinitely many

D

no value of k satifies the requirement

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The correct Answer is:
D
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OBJECTIVE RD SHARMA-MEAN VALUE THEOREMS-Exercise
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  2. Let (a0)/(n+1)+(a1)/n+(a2)/(n-1)++(a(n-1))/2+an=0. Show that there e...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  17. For the function f(x) = x + 1/x, x in [1,3] , the value of c for me...

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  18. If from Largrange's mean value theorem, we have f(x'(1))=(f'(b)-f(a))...

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  19. Rolle's theorem is applicable in case of phi(x) = a^sin x,a>0 in

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  20. The value of c in Rolle's theorem when f(x)=2x^(3)-5x^(2)-4x+3, x in [...

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