Home
Class 11
MATHS
If alpha and beta are the roots of ax^2+...

If `alpha` and `beta` are the roots of `ax^2+bx+c`=0, then the equation `ax^2-bx(x-1)+c(x-1)^2`=0 has roots

A

`(alpha)/(1-alpha),(beta)/(1-beta)`

B

`(1-alpha)/(alpha),(1-beta)/(beta)`

C

`(alpha)/(1+alpha),(beta)/(1+beta)`

D

`(alpha+1)/(alpha),(beta+1)/(beta)`

Text Solution

Verified by Experts

The correct Answer is:
C
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

If alpha and beta are roots of ax^(2)+bx+c=0 then the equationnwhose roots are alpha^(2)andbeta^(2) is

If alpha and beta are the roots of ax^(2)+bx+cid=0 find the equation whose rootsare alpha^(-3), beta^(-3) .

If alpha , beta , gamma are the roots of the equation 9x^(3)-7x+6=0 then the equation x^(3)+Ax^(2)+Bx+C=0 has roots 3alpha+2 , 3beta+2 , 3gamma+2 , where

If alpha and beta be the roots of the equation 5x^2+bx+c=0 Show that 5x^2+bx+c=5(x-alpha)(x-beta) Show also that for all real values of x the expression 5x^2+bx+c cannot be negative if alpha and beta are real and equal

If alpha and beta be the roots of the equation 5x^2+bx+c=0 Show that 5x^2+bx+c=5(x-alpha)(x-beta) Show also that for all real values of x the expression 5x^2+bx+c cannot be negative if alpha and beta are conjugate complex.

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

If alpha and beta are roots of the equation ax^2+bx+c =0 and, if px^2+qx+r =0 has roots (1-alpha)/alpha and (1-beta)/beta , then r is equal is

If alpha,beta are the roots of the quadratic equation ax^2+bx+c=0 and 3b^2=16ac then

If alpha,beta are the roots of the quadratic equation ax^(2)+bx+c=0and3b^(2)=16ac then-

If alpha, beta are the roots of the quadratic equation ax^(2)+bx+c=0 and 3b^(2)=16 ac then

PATHFINDER-QUADRATIC EQUATION AND EXPRESSION-QUESTION BANK
  1. If the sum of the roots of ax^2+bx+c=0 is equal to the sum of their s...

    Text Solution

    |

  2. If x is real number, then the minimum value of x^2+x+1 is

    Text Solution

    |

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

    Text Solution

    |

  4. If the quadratic equations ax^2+2cx+b=0 and ax^2+2bx+c=0 (bne0) have a...

    Text Solution

    |

  5. The value of 'a' for which the equation x^3+ax+1=0 and x^4+ax^2+1=0, w...

    Text Solution

    |

  6. The coefficient of 'x' in the quadratic equation ax^2+bx+c=0 was wrong...

    Text Solution

    |

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

    Text Solution

    |

  8. If one root of the equation x^2+px+12=0 is 4, while the equation x^2+p...

    Text Solution

    |

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

    Text Solution

    |

  10. If one root of the equation x^2+(1-3i)x-2(1+i)=0is -1+i, then the oth...

    Text Solution

    |

  11. If alpha,beta roots of ax^2+bx+c=0. Find the quadratic equation whose ...

    Text Solution

    |

  12. If alpha,beta be the two roots of the equation x^2+x+1=0, then the equ...

    Text Solution

    |

  13. The harmonic mean of the roots of the equation (5+sqrt)x^2-(4+sqrt5)x+...

    Text Solution

    |

  14. The equation x^3+5x^2+px+q=0 and x^3+7x^2+px+r=0 have two roots in com...

    Text Solution

    |

  15. If the roots of x^2+bx+c=0 are both real and greater than unity, then ...

    Text Solution

    |

  16. Value of p, so that 6 lies between roots of the equation x^2+2(p-3)x+9...

    Text Solution

    |

  17. Ifx^2-(a-3)x+a=0 has at least one positive root,then

    Text Solution

    |

  18. If the roots of the equation x^2-2ax+a^2 + a-3=0 are less than 3 then

    Text Solution

    |

  19. The number of solutions of log2(x-1)=2log2(x-3) is

    Text Solution

    |

  20. If x=(sqrt13+2sqrt3), then x+1/x is equal to ?

    Text Solution

    |