Home
Class 12
MATHS
IF alpha,beta and gamma, delta are the r...

IF `alpha,beta and gamma, delta` are the roots of the equations `x^2-bx+c=0` and `x^2-px+q=0` respectively, show that , `(alpha-gamma)(beta-delta) -alpha.gamma - beta. delta=(c+q)-bp`.

Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

    CHHAYA PUBLICATION|Exercise EXERCISE 5A(Long Answer type question)|56 Videos
  • QUADRATIC EQUATIONS

    CHHAYA PUBLICATION|Exercise EXERCISE 5B(Multiple Choice type question)|5 Videos
  • QUADRATIC EQUATIONS

    CHHAYA PUBLICATION|Exercise EXERCISE 5A(Very Short Answer type Question)|30 Videos
  • PROPERTIES OF TRIANGLE

    CHHAYA PUBLICATION|Exercise Assertion- Reason Type:|2 Videos
  • QUESTION PAPER -2018

    CHHAYA PUBLICATION|Exercise WBJEE|45 Videos

Similar Questions

Explore conceptually related problems

IF alpha,beta and gamma,delta be the roots of the equation x^2+px-r=0 and x^2+px+r=0 respectively, prove that (alpha-gamma)(alpha-delta)=(beta-gamma)(beta-delta)

IF alpha,beta and gamma,delta be the roots of the equation x^2-bx+c=0 and x^2-cx+b=0 respectively, form the equation whose roots are (1/(alphagamma)+1/(betadelta)) and (1/(alphadelta)+1/(betagamma)) .

If alpha,beta,gamma are the roots of the equation x^3+p x^2+q x+r=0, then find he value of (alpha-1/(betagamma))(beta-1/(gammaalpha))(gamma-1/(alphabeta)) .

If alpha,beta,gamma are the roots of the equation x^3-p x+q=0, then find the cubic equation whose roots are alpha/(1+alpha),beta/(1+beta),gamma/(1+gamma) .

If alpha , beta , gamma are the roots of the equation px^3 - qx + r = 0 , then the value of alpha + beta + gamma is

If alpha,beta,gamma are the roots of the equation x^3+x+1=0 , then the value of alpha^3+beta^3+gamma^3 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 alphaandbeta be the roots of the quadratic equation px^(2)-qx+q=0 , then show that sqrt((alpha)/(beta))+sqrt((beta)/(alpha))-sqrt((q)/(p))=0 .

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

Let P (x)=x ^(6) -x ^(5) -x ^(3) -x ^(2) -x and alpha, beta, gamma, delta are the roots of the equation x ^(4) -x ^(3)-x ^(2) -1=0, then P (alpha ) + P (beta) +P (gamma) + P(delta)=

CHHAYA PUBLICATION-QUADRATIC EQUATIONS-EXERCISE 5A(Short answer type question)
  1. IF alpha and beta be the roots of the equation 5x^2+7x+3=0 , find the ...

    Text Solution

    |

  2. IF p and q are the roots of the equation ax^2+bx+c=0 find the value of...

    Text Solution

    |

  3. IF alpha,beta and gamma, delta are the roots of the equations x^2-bx+c...

    Text Solution

    |

  4. If the roots of the equation ax^2-bx+a=0 be alpha and beta, show that ...

    Text Solution

    |

  5. IF alpha and beta be the roots of the equation 2x^2+x+1=0 find the equ...

    Text Solution

    |

  6. IF alpha and beta are the roots of the equation x^2+alphax+beta=0 then...

    Text Solution

    |

  7. If the roots of the equation ax^2+bx+c=0 be alpha and beta, find the e...

    Text Solution

    |

  8. IF alpha,beta be the roots of the equation x^2+px+q=0, show that 1/(a...

    Text Solution

    |

  9. IF the roots of the equation ax^2+bx+c=0 be alpha and beta, find the e...

    Text Solution

    |

  10. Form the quadratic equation whose roots alpha and beta satisfy the rel...

    Text Solution

    |

  11. Form the quadratic equation whose roots are the squares of the roots o...

    Text Solution

    |

  12. Form the quadratic equation whose roots are reciprocals of the roots o...

    Text Solution

    |

  13. IF 3a^2=4a-5and 3b^2=4b-5 where ane b, find the value of a^2+b^2.

    Text Solution

    |

  14. IF 3p^2=5p+2and 3q^2=5q+2 where pne q , obtain the equation whose root...

    Text Solution

    |

  15. IF alpha and beta be the roots of the equation x^2-4x+10=0, find the e...

    Text Solution

    |

  16. If p and q are the roots of the equation 3x^2+6x+2=0, show that the eq...

    Text Solution

    |

  17. If the sum of the roots of a quadratic equation is 2 and the sum of th...

    Text Solution

    |

  18. If the sum of the roots of the equation x^2-px+q=0 be three times thei...

    Text Solution

    |

  19. If the roots of the equation ax^2+bx+c=0 are in the ratio 3:4 show tha...

    Text Solution

    |

  20. If one root of the equation x^2+(5a+2)x+5a+2=0 is five times the other...

    Text Solution

    |