Home
Class 11
MATHS
Ifalpha,beta be the roots of x^2-a(x-1)+...

If`alpha,beta` be the roots of `x^2-a(x-1)+b`=0,then the value of `1/(alpha^2-aalpha)+1/(beta^2-abeta)+2/(a+b)` is

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise All Questions|363 Videos
  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

If alpha and beta are the roots of x^2-x+1=0 ,then the value of alpha^(2013)+beta^(2013) is equal to

If alphaand beta are the roots of x^(2)-x+1=0 ,then the value of alpha^(2013)+beta^(2013) is equal to -

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

If alphaandbeta be the roots of the equation 3x^(2)+8x+2=0 , then the value of ((1)/(alpha)+(1)/(beta))

If alpha,beta are the roots of the equation a x^2+b x+c=0, then the value of (aalpha^2+c)/(aalpha+b)+(abeta^2+c)/(abeta+b) is a. (b(b^2-2a c))/(4a) b. (b^2-4a c)/(2a) c. (b(b^2-2a c))/(a^2c) d. none of these

If alpha, beta are the roots of x^(2) - px + q = 0 and alpha', beta' are the roots of x^(2) - p' x + q' = 0 , then the value of (alpha - alpha')^(2) + (beta -alpha')^(2) + (alpha - beta')^(2) + (beta - beta')^(2) is

IF alpha,beta be the roots of the equation ax^2+bx+c=0 find the value of (aalpha^2)/(balpha+c)-(abeta^2)/(b beta+c)

If alpha and beta be the roots of equation x^(2) + 3x + 1 = 0 then the value of ((alpha)/(1 + beta))^(2) + ((beta)/(1 + alpha))^(2) is equal to

If alpha, beta be the roots of the equation x^(2)+x+1=0 , the value of alpha^(4)beta^(4)-alpha^(-1)beta^(-1) is

If alphaandbeta be the roots of the equation 5x^(2)+2x-3=0 , then find the values of ((1)/(alpha)+(1)/(beta))

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If alpha,beta are roots of x^2+p x+1=0a n dgamma,delta are the roots o...

    Text Solution

    |

  2. If he roots of the equation12 x^2-m x+5=0 are in the ratio 2:3 then fi...

    Text Solution

    |

  3. Ifalpha,beta be the roots of x^2-a(x-1)+b=0,then the value of 1/(alpha...

    Text Solution

    |

  4. The equation formed by decreasing each root of ax^(2)+bx+c=0 by 1 is2x...

    Text Solution

    |

  5. If the sum of the roots of an equation is 2 and the sum of their cubes...

    Text Solution

    |

  6. If x is real and (x^2+2x+c)/(x^2+4x+3c) can take all real values, of t...

    Text Solution

    |

  7. Find the range of f(x)=sqrt(x-1)+sqrt(5-xdot)

    Text Solution

    |

  8. If x^2+ax+bc=0 and x^2+bx+ac=0 have a common root, show their other ro...

    Text Solution

    |

  9. Let alpha,beta are the roots of x^2+b x+1=0. Then find the equation wh...

    Text Solution

    |

  10. Find the greatest value of a non-negative real number lambda for which...

    Text Solution

    |

  11. If a ,b ,c in R such that a+b+c=0a n da!=c , then prove that the root...

    Text Solution

    |

  12. Evaluate: i^(135) (-sqrt(-1))^(4n+3),n in N sqrt(-25)+3sqrt(-4)+...

    Text Solution

    |

  13. If the equation (a-5)x^2+2(a-10)x+a+10=0 has roots of opposite sign, t...

    Text Solution

    |

  14. If alphaa n dbeta are the roots of ax^2+bx+c=0a n dSn=alpha^n+beta^n,...

    Text Solution

    |

  15. If alpha is a root of the equation 4x^2+2x-1=0, then prove that 4alp...

    Text Solution

    |

  16. If both the roots of x^2-a x+a=0 are greater than 2, then find the val...

    Text Solution

    |

  17. If (y^2-5y+3)(x ^2+x+1)<2x for all x in R , then find the interval in...

    Text Solution

    |

  18. Find the values of 'a' which 4^t-(a-4)2^t+9/4alt0,foralltin(1,2)

    Text Solution

    |

  19. Find the number of positive integral values of k for which kx ^(2) +(k...

    Text Solution

    |

  20. If x^2+2ax+a lt 0 AA x in [1, 2] then find set of all possible values ...

    Text Solution

    |