Home
Class 11
MATHS
Let alpha , beta be the roots of x^2-x+p...

Let `alpha` , `beta` be the roots of `x^2-x+p=0 and gamma,delta` be the roots of `x^2-4x+q=0 `. If `alpha,beta,gamma` are in GP , then the integer values of p and q respectively are:

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|9 Videos
  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

Let alpha,beta be the roots of the equation x^2-4x+A=0 and gamma,delta be the roots of the equation x^2-36x+B=0 . If alpha,beta,gamma and delta are In G.P. having positive common ratio, find the value of A and B.

Let alpha,beta be the roots of the equation x^2-3x+a=0 and gamma,delta the roots of the equation x^2-12x+b=0 . If alpha,beta,gamma and delta are in G.P. having positive common ratio, then find the values of a and b.

If alpha,beta are the roots of x^2-px+1=0 and gamma is a root of x^2+px+1=0 , then (alpha+gamma)(beta+gamma) is

If alpha,beta are the roots x^(2)-px+1=0 and gamma "is a root of "x^(2)+px+1=0 ,then (alpha+gamma)(beta+gamma) is -

Let alpha_1,beta_1 be the roots x^2-6x+p=0a n d alpha_2,beta_2 be the roots x^2-54 x+q=0dot If alpha_1,beta_1,alpha_2,beta_2 form an increasing G.P., then sum of the digits of the value of (q-p) is ___________.

If alpha,beta are the roots x^2+px+q =0 and gamma,delta are the roots of x^2+rx+s =0, evaluate (alpha-gamma)(alpha-delta)(beta-gamma)(beta-delta) in terms of p,q,r and s. Deduce the condition that the equation may have a common root.

If alpha,beta be the roots x^2+px-q=0 and gamma,delta be the roots of x^2+px+r=0, p+rphi0 ,then ((alpha-gamma)(alpha-delta))/((beta-gamma)(beta-delta)) is equal to

If alpha,beta are the roots of x^2+px+q =0 and also of x^(2n)+p^n x^n+q^n=0 and if alpha/beta,beta/alpha are root of x^n+1+(x+1)^n =0, then n is

If alpha,beta are roots of x^2+p x+1=0a n dgamma,delta are the roots of x^2+q x+1=0 , then prove that q^2-p^2=(alpha-gamma)(beta-gamma)(alpha+delta)(beta+delta) .

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

CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. If 1/1^2+1/2^2+1/3^2+.... upto infty=pi^2/6 , then, find 1/1^2+1/3^2+1...

    Text Solution

    |

  2. Coefficient of x^(18) in (1+x+2x^2+3x^3++18 x^(18))^2 equal to 995 b. ...

    Text Solution

    |

  3. Let alpha , beta be the roots of x^2-x+p=0 and gamma,delta be the root...

    Text Solution

    |

  4. If the sum of the first 2n terms of the AP 2,5,8.....is equal to the s...

    Text Solution

    |

  5. Statement 1: If the arithmetic mean of two numbers is 5/2 geometric ...

    Text Solution

    |

  6. Number of positive integral ordered pairs of (x,y), so that 8,x,y are ...

    Text Solution

    |

  7. If three positive real numbers a,b ,c are in A.P such that a b c=4 , t...

    Text Solution

    |

  8. Consider an infinite geometric series with first term a and common rat...

    Text Solution

    |

  9. The maximum sum of the series 20+19 1/3+18 2/3+...... is (A) 310 (B) ...

    Text Solution

    |

  10. The sum of n terms of a progression is (2^n-1). Show that it is a GP a...

    Text Solution

    |

  11. Let a1 , a2 ,... be in harmonic progression with a1 = 5 and a20 = 25. ...

    Text Solution

    |

  12. An infinite G.P. has first term as a and sum 5, then a belongs to a) |...

    Text Solution

    |

  13. Let Ssub(0,pi) denote the set of values of x satisfying the equation 8...

    Text Solution

    |

  14. Find the number of terms of a G.P. whose first term is ¾, common ratio...

    Text Solution

    |

  15. In an A.P. (with usual notations) : (i) given a = 7, a13 = 35, find ...

    Text Solution

    |

  16. Find the geometric progression whose 4th term is 54 and the 7th term i...

    Text Solution

    |

  17. The first term of G.P. is 27 and 8th term is 1/81. Find the sum of its...

    Text Solution

    |

  18. The greatest integer by which 1+sum(r=1)^(30)rxxr ! is divisible is a....

    Text Solution

    |

  19. (lim)(ntooo)sum(r=1)^n r/(1xx3xx5xx7xx9xx.....xx(2r+1)) is equal to 1/...

    Text Solution

    |

  20. Value of (1+1/3)(1+1/(3^2))(1+1/(3^4))(1+1/(3^8))........oo is equal ...

    Text Solution

    |