Home
Class 12
MATHS
If alpha,beta are roots of x^2+-p x+1=0a...

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)` .

A

`p^(2)-q^(2)`

B

`q^(2)-p^(2)`

C

`p^(2)`

D

`q^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • THEORY OF QUADRATIC EQUATIONS

    ML KHANNA|Exercise Problem Set - 1 (True And False)|3 Videos

  • THEORY OF QUADRATIC EQUATIONS

    ML KHANNA|Exercise Problem Set - 1 (Fill In The Blanks)|4 Videos

  • THE PARABOLA

    ML KHANNA|Exercise MISCELLANEOUS EXERCISE (Assertion/ Reason)|1 Videos

  • TRIGONOMETRICAL EQUATIONS

    ML KHANNA|Exercise SELF ASSESSMENT TEST |27 Videos

Similar Questions

Explore conceptually related problems

If alpha,beta are roots of x^(2)+-px+1=0 and gamma,delta are the roots of x^(2)+qx+1=0 ,then prove that q^(2)-p^(2)=(alpha-gamma)(beta-gamma)(alpha+delta)(beta+delta)

If alpha and beta are the roots of x^(2) +px+q=0 and gamma, delta are the roots of x^(2)+rx+s=0, then evaluate (alpha-gamma)(beta-gamma) (alpha-delta) (beta-deta) in terma of p,q, r and s.

If alpha and beta are the roots of x^(2) +px+q=0 and gamma , delta are the roots of x^(2) +rx+x=0 , then evaluate (alpha - gamma ) ( beta - gamma ) (alpha - delta ) ( beta - delta) in terms of p,q,r and s .

If alpha and beta are the roots of the equation x^(2) +px+1=0 , gamam , delta are the roots of (x^(2) +qx+1=0 , then , find ( alpha-gamma ) (beta - gamma ) ( alpha + delta )(beta + delta )

If alpha,beta are the roots of x^(2)+ax-b=0 and gamma,delta are the roots of x^(2)+ax+b=0 then (alpha-gamma)(alpha-delta)(beta-gamma)(beta-delta)=

If alpha,beta are the roots of x^(2)+px+q=0and gamma,delta are the roots of x^(2)+px+r=0, then ((alpha-gamma)(alpha-delta))/((beta-gamma)(beta-delta))= a.1b.q c.r d.q+r

If alpha,beta are the roots of x^(2)+px+q=0and 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, ands.Deduce the condition that the equation has a common root.

ML KHANNA-THEORY OF QUADRATIC EQUATIONS -Self Assessment Test
  1. If alpha,beta are roots of x^2+-p x+1=0a n dgamma,delta are the roots ...

    Text Solution

    |

  2. If the equation x^(2)-(2+m)x +(m^(2)-4m+4)=0 has equal roots then the ...

    Text Solution

    |

  3. The number of real solutions of the equation |x|^(2)-3|x|+2=0 is :

    Text Solution

    |

  4. Find the number of solution of the equation e^(sinx)-e^(-sinx)-4=0

    Text Solution

    |

  5. The roots of the equation (p-q) x^(2)+(q-r) x+(r-p)=0 are

    Text Solution

    |

  6. If one root of x^(2) + px+12 = 0 is 4, while the equation x ^(2)...

    Text Solution

    |

  7. Let alpha and beta are the roots of the equation x^(2) + x + 1 = 0 The...

    Text Solution

    |

  8. If the quadratic equation x^(2) +ax +b =0 and x^(2) +bx +a =0 (a ne b...

    Text Solution

    |

  9. If the roots of the equation x^2-8x+a^2-6a=0 are real distinct, then f...

    Text Solution

    |

  10. The value of k for which the equation x^(2)-(3k-1)x+2k^(2)+2k=11 have ...

    Text Solution

    |

  11. if 2 = I sqrt3 be a root of the equation x^(2) + px + q =0, where p ...

    Text Solution

    |

  12. The number of solutions of the pair of equations 2s in^2theta-cos2thet...

    Text Solution

    |

  13. If alpha, beta are roots of the equations Ax^(2)+Bx+C=0. Then value of...

    Text Solution

    |

  14. If the equation x^(2)+px+q=0 and x^(2)+qx+p=0 have a common root then ...

    Text Solution

    |

  15. If alpha and beta (alpha lt beta) are the roots of the equation x^(2) ...

    Text Solution

    |

  16. If 2a+3b+6c=0, then prove that at least one root of the equation a x^2...

    Text Solution

    |

  17. If the roots of the equation (x^2-b x)/(a x-c)=(m-1)/(m+1) are equal t...

    Text Solution

    |

  18. If sin alpha, cos alpha are the roots of the equation ax^(2)+bx+c=0, t...

    Text Solution

    |

  19. If alpha, beta are the roots of x^(2)-ax+b =0 and If alpha^(n)+beta^(n...

    Text Solution

    |

  20. The value of a for which one root of the quadratic equation (a^2-5a+3)...

    Text Solution

    |

  21. If a,b, c are in G.P., then the equations ax^(2) + 2bx + c = 0 and dx^...

    Text Solution

    |