Home
Class 12
MATHS
Let alpha(a) and beta(a) be the roots of...

Let `alpha(a)` and `beta(a)` be the roots of the equation `((1+a)^(1/3)-1)x^2 +((1+a)^(1/2)-1)x+((1+a)^(1/6)-1)=0` where `agt-1` then `lim_(a->0^+)alpha(a)` and `lim_(a->0^+)beta(a)`

A

`-5/2` and 1

B

`-1/2` and -1

C

`-7/2` and 2

D

`-9/2` and 3

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise JEE main (Archive)|51 Videos

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos

  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|81 Videos

Similar Questions

Explore conceptually related problems

Let alpha, and beta are the roots of the equation x^(2)+x +1 =0 then

Let alpha, beta are the roots of the equation x^(2)+x+1=0 , then alpha^3-beta^3

If alpha and beta are roots of the equation x^(2)+x+1=0 , then alpha^(2)+beta^(2) is equal to

If alpha and beta are roots of the equation 2x^(2)-3x-5=0 , then the value of (1)/(alpha)+(1)/(beta) is

If alpha , beta , gamma are roots of the equation x^3 + ax^2 + bx +c=0 then alpha^(-1) + beta^(-1) + gamma^(-1) =

If alpha, beta, gamma are the roots of the equation x^(3) + ax^(2) + bx + c = 0, "then" alpha^(-1) + beta^(-1) + gamma^(-1)=

If alpha,beta are the roots of the equation x^(2)+x+1=0 , find the value of alpha^(3)-beta^(3) .

If alpha and beta are roots of the equation ax^2+bx +c=0 , then lim_(xrarralpha) (1+ax^2+bx+c)^(1//x-alpha) , is

Let alpha and beta be the roots of x^(2)+x+1=0 , then the equation whose roots are alpha^(2020) and beta^(2020) is

Let alpha and beta , be the roots of the equation x^2+x+1=0 . The equation whose roots are alpha^19 and beta^7 are:

VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS-JEE Advanced (Archive)
  1. Let f(x) = {{:(x^(2)|"cos"(pi)/(x)|",",x ne 0","x in R),(0",",x = 0):}...

    Text Solution

    |

  2. If underset(xtooo)lim((x^(2)+x+1)/(x+1)-ax-b)=4, then

    Text Solution

    |

  3. Let alpha(a) and beta(a) be the roots of the equation ((1+a)^(1/3)-1)x...

    Text Solution

    |

  4. Check the differentiability if f(x) = min. {1, x^(2), x^(3)}.

    Text Solution

    |

  5. Let f(x) be a non-constant twice differentiable function defined on (-...

    Text Solution

    |

  6. Let L=("lim")(xvec0)(a-sqrt(a^2-x^2)-(x^2)/4)/(x^4),a > 0. IfLi sfin i...

    Text Solution

    |

  7. For the function f(x)=x cos ""1/x, x ge 1 which one of the following i...

    Text Solution

    |

  8. Let f : R rarr R be a function such that f(x+y) = f(x) + f(y), AA x, y...

    Text Solution

    |

  9. if f(x) ={{:(-x=(pi)/(2),xle -(pi)/(2)),(- cos x, -(pi)/(2)lt x ,le 0...

    Text Solution

    |

  10. Let f(x)=xsinpix ,x > 0. Then for all natural numbers n ,f^(prime)(x) ...

    Text Solution

    |

  11. Let f:[a,b]to[1,oo) be a continuous function and let g:RtoR be defined...

    Text Solution

    |

  12. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

    Text Solution

    |

  13. Let F : R to R be a thrice differentiable function . Suppose that F(...

    Text Solution

    |

  14. Given that for each a epsilon(0,1),lim(hto 0^(+)) int(h)^(1-h)t^(-a)(1...

    Text Solution

    |

  15. Given that for each a epsilon(0,1),lim(hto 0^(+)) int(h)^(1-h)t^(-a)(1...

    Text Solution

    |

  16. Let fandg be real valued functions defined on interval (-1,1) such tha...

    Text Solution

    |

  17. Let alpha,betainR be such that underset(xto0)lim(x^(2)sin(betax))/(alp...

    Text Solution

    |

  18. If f(x) is a polynomial of degree 4 having extremum at x=1,2 and lim(x...

    Text Solution

    |

  19. Let f:[1,oo] be a differentiable function such that f(1)=2. If int1...

    Text Solution

    |

  20. The largest value of the non-negative integer a for which lim(xto1) ...

    Text Solution

    |