Home
Class 11
MATHS
Let p,q be real numbers. If alpha is the...

Let p,q be real numbers. If `alpha` is the root of `x^2+3p^2x+5q^2=0`, `beta` is a root of `x^2+9p^2x+15q^2=0` and `0ltalphaltbeta`, then the equation `x^2+6p^2x+10q^2=0` has a root `gamma` that always satisfies.

A

`gamma=alpha/4+beta`

B

`betaltgamma`

C

`gamma=alpha/2+beta`

D

`alphaltgammaltbeta`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATION

    PATHFINDER|Exercise QUESTION BANK|19 Videos

  • RECTANGULAR CO-ORDINATES

    PATHFINDER|Exercise QUESTION BANK|27 Videos

Similar Questions

Explore conceptually related problems

Let p ,q be real numbers . If alpha" is a root of x^(2)+3p^(2)x+5q^(2)=0,beta" is a root of "x^(2)+9p^(2)+15q^(2)=0and0ltalphaltbeta" then the equation" x^(2)+6p^(2)+10q^(2)=0 has a root gamma that always satisfies -

If p and q are the roots of the equation x^2+px+q =0, then

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

For what real 'p' do the roots of x^2-2x-p^2+1=0 lie between the roots of x^2-(p+1)x+(p-1)=0 ?

IF p^3-q(3p-1)+q^2=0 , find the relation between the roots of the equation x^2+px+q=0 .

IF alpha and beta be the roots of the equation x^2+px+q=0 show that alpha/beta is a root of the equation qx^2-(p^2-2q)x+q=0 .

If , p , q are the roots of the equation x^(2)+px+q=0 , then

If sec alpha and "cosec" alpha are the roots of x^(2)- px+q=0 then show that p^(2)=q(q+2)

If sec alpha and cosec alpha are the roots of x^2-px+q=0 then prove that p^2=q(q+2)

PATHFINDER-QUADRATIC EQUATION AND EXPRESSION-QUESTION BANK
  1. In a Delta ABC, tanA and tanB are roots of pq(x^2+1)=r^2x. Then DeltaA...

    Text Solution

    |

  2. If alpha,beta are the roots of the quadratic equation x^2+px+q=0, then...

    Text Solution

    |

  3. Let p,q be real numbers. If alpha is the root of x^2+3p^2x+5q^2=0, bet...

    Text Solution

    |

  4. Let alpha,beta be the roots of x^2-x-1=0 and Sn=alpha^n+beta^n, for al...

    Text Solution

    |

  5. If alpha,beta are the roots fo ax^2+bx+c=0 (ane0) and alpha+h, beta+h ...

    Text Solution

    |

  6. The equation sqrt(x+1)-sqrt(x-1)=sqrt(4x-1) has

    Text Solution

    |

  7. If a, b and c are positive numbers in a G.P., then the roots of the qu...

    Text Solution

    |

  8. If the equation x^2+2x+3=0 and ax^2+bx+c=0 , a, b, c in R, have a comm...

    Text Solution

    |

  9. If alpha and beta are the roots of x^2-x+1=0,then the value of alpha^(...

    Text Solution

    |

  10. If alpha,beta are the roots of the quadratic equation x^2+ax+b=0, (bne...

    Text Solution

    |

  11. Let p(x) be a quadratic polynomial with constant term 1. Suppose p(x) ...

    Text Solution

    |

  12. If alpha,beta are the roots of the quadratic equation ax^2+bx+c=0 and ...

    Text Solution

    |

  13. Let sinalpha,cosalpha, be the roots of the equation x^2-bx+c=0. Then w...

    Text Solution

    |

  14. What is the calorific value of 80 gms of carbohydrate, 15 gms of prote...

    Text Solution

    |

  15. The equation e^(sin x) -e^(-sin x)-4=0 has

    Text Solution

    |

  16. The equations x^2+x+a=0 and x^2+ax+1=0 have a common real root

    Text Solution

    |

  17. If (alpha+sqrtbeta) and (alpha-sqrtbeta) are the roots of the equation...

    Text Solution

    |

  18. If a, b, c are in arithmetic progression, then the roots of the equati...

    Text Solution

    |

  19. The quadratic equation 2x^2-(a^3+8a-1)x+a^2-4a=0 possesses roots of op...

    Text Solution

    |

  20. A value of b for which the equations x^2+bx-1=0, x^2+x+b =0 have one r...

    Text Solution

    |