Home
Class 12
MATHS
If alpha,beta are the roots of the equat...

If `alpha,beta` are the roots of the equation `x^2-p x+q=0,` prove that `(log)_e(1+p x+q x^2)=(alpha+beta)x-(alpha^2+beta^2)/2x^2+(alpha^3+beta^3)/3x^3+`

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP ENGLISH|Exercise All Questions|15 Videos
  • MATRICES

    RESONANCE DPP ENGLISH|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

If alpha and beta are the roots of the equation x^2-px + q = 0 then the value of (alpha+beta)x -((alpha^2+beta^2)/2)x^2+((alpha^3+beta^3)/3)x^3+... is

If alpha and beta are the roots of the equation x^2-px + q = 0 then the value of (alpha+beta)x -((alpha^2+beta^2)/2)x^2+((alpha^3+beta^3)/3)x^3+... is

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

If alpha,beta are the roots of the equation x^(2)-2x-1=0 , then what is the value of alpha^(2)beta^(-2)+alpha^(-2)beta^(2) ?

If alpha,beta are the roots of the equation 8x^2-3x+27=0, then the value of (alpha^2/beta)^(1/3)+(beta^2/alpha)^(1/3) is

If alpha , beta , gamma are the roots of the equation x^3 +4x^2 -5x +3=0 then sum (1)/( alpha^2 beta^2)=

If alpha and beta are the roots of the equation 2x^(2) - 3x + 4 = 0 , then alpha^(2) + beta^(2) = ____

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

If alpha,beta are the roots of the equation x^(2)+px+q=0 , find the value of (a) alpha^(3)beta+alphabeta^(3) (b) alpha^(4)+alpha^(2)beta^(2)+beta^(4) .

If alpha , beta are the roots of the equation x^(2)-px+q=0 , then (alpha^(2))/(beta^(2))+(beta^(2))/(alpha^(2)) is equal to :

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. Two aeroplanes I and II bomb a target in succession. The probabilitie...

    Text Solution

    |

  2. The lines 3x+4y=9&4x-3y+12=0 intersect at Pdot The first line intersec...

    Text Solution

    |

  3. If alpha,beta are the roots of the equation x^2-p x+q=0, prove that (l...

    Text Solution

    |

  4. A bag initially contains 1 red and 2 blue balls. An experiment consi...

    Text Solution

    |

  5. If the circles x^2+y^2-2x-2y-7=0 and x^2+y^2+4x+2y+k=0 cut orthogonall...

    Text Solution

    |

  6. The length of transverse common tangent of the circles x^2+y^2=1and(x-...

    Text Solution

    |

  7. The function f(x)=sqrt(a x^3+b x^2+c x+d) has its non-zero local mini...

    Text Solution

    |

  8. The area of the region given by x^2+y^2-6y<=0&y<=x is (9pi-9)/4 b. ...

    Text Solution

    |

  9. Let f(x) be a differentiable function and f(a)=f(b)=0 (alpha ltbeta), ...

    Text Solution

    |

  10. A determinant is chosen at random from the set of the determinants of ...

    Text Solution

    |

  11. Let vec a=2 hati+hat j+ hat k , vec b=hat i+2hat j- hatk and a unit v...

    Text Solution

    |

  12. A die is rolled 4 times. The probability of getting a larger number ...

    Text Solution

    |

  13. If (d)/(dx)((1+x^2+x^4)/(1+x+x^2)) = a+bx , find the values of a and ...

    Text Solution

    |

  14. There are 4 urns. The first urn contains 1 white and 1 black ball, the...

    Text Solution

    |

  15. The number of ways in which 5 X's can be placed in the squares of the ...

    Text Solution

    |

  16. If S be the sum, p the product and R the sum of the reciprocals of n t...

    Text Solution

    |

  17. If f^(prime)(x)=sqrt(2x^2-1) and y=f(x^2) , then find (dy)/(dx) at x=1...

    Text Solution

    |

  18. First, second and sevents terms of an A.P. (all the terms are distinct...

    Text Solution

    |

  19. "If "xsqrt(1+y)+ysqrt(1+x)=0," prove that "(dy)/(dx)=-(1)/((x+1)^(2)).

    Text Solution

    |

  20. There is a certain sequence of positive real numbers. Beginning from t...

    Text Solution

    |