Home
Class 12
MATHS
Assertion (A) : If 1,2,3 are the root...

Assertion (A) : If 1,2,3 are the roots of `ax^3 + bx ^2 +cx +d=0` then the roots of ` ax^3 +2bx^2 + 4 cx + 8d =0` are =0 are ` 2,4,6`
Reason (R ) : the equation whose roots are k times the roots of the equation `f(x) =0` is ` f((x )/(k ))=0`

A

both A and R are true R is the correct explanation of A

B

both A and R are true and R is not correct explanation of A

C

A is true and R is false

D

A is false and R is true

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    AAKASH SERIES|Exercise EXERCISE-III|46 Videos

  • THEORY OF EQUATIONS

    AAKASH SERIES|Exercise EXERCISE-I|47 Videos

  • SYSTEM OF CIRCLES

    AAKASH SERIES|Exercise EXERCISE 2.2|22 Videos

  • TRANSFORMATIONS AND INDENTITIES

    AAKASH SERIES|Exercise PRACTIVE EXERCISE|36 Videos

Similar Questions

Explore conceptually related problems

If 1, -2, 3 are the roots of ax^(3) + bx^(2) + cx + d = 0 then the roots of ax^(3) + 3bx^(2) + 9cx + 27d = 0 are

The equation whose roots are 'K' times the roots of the equation ax^(2)+bx+c=0 is

If 2, - 2, 4 are the roots of ax^(3) + bx^(2) + cx + d = 0 then the roots of 8ax^(3) + 4bx^(2) + 2cx + d = 0 are

The equation whose roots are the cubes of the roots of the equation ax ^2+bx +c=0 is

Assertion (A ) : If 1,2,3 are the roots of ax^3 +bx^2 + cx + +d =0 then roots of ax^3 + 2 bx^2 + 4 cx +8d =0 are 2,4,6 Reason (R ) : The equation whose roots are k times the roots of the equation f(x) =0 Is f(x//k) =0 then the true statment among the following is :

If 1,2,3 are the roots of ax^3 +bx^2 + cx +d=0 then the roots of ax sqrt(x) + bx +c sqrt (x ) +d=0 are

If 2,5,7,-4 are the roots of ax^4 + bx^3 + cx^2 + dx +e=0 then the roots of ax^4 - bx^3 + cx^2 -dx +e=0 are

If the roots of ax^3 + bx^2 + cx +d=0 are in G.P then the roots of ak^3 x^3 +bk^2 x^2 + ck x+d=0 are in

AAKASH SERIES-THEORY OF EQUATIONS-EXERCISE-II
  1. If alpha , beta , gamma are the roots of x^3 -6x -4=0 then th...

    Text Solution

    |

  2. If alpha , beta , gamma are the roots of x^3 + 4x +1 =0 then th...

    Text Solution

    |

  3. If alpha , beta , gamma are the roots of the equation x^3 +px...

    Text Solution

    |

  4. Remove the third term from the equation x^4 +2x^3 -12 x^2 +2x -1...

    Text Solution

    |

  5. Number of transformed equations of x^3 +2x^2 +x+1=0 by eliminating...

    Text Solution

    |

  6. The transformed equation x^3 -5/2 x^2 -(7)/(18 ) x+(1)/( 108 )...

    Text Solution

    |

  7. The transformed equation with integer co-effcients whose roots ...

    Text Solution

    |

  8. If the equation whose roots are p times the roots of x^4 +2x^...

    Text Solution

    |

  9. Let alpha ne 1 be a real root of the equation x^(3) - ax^(2) + ax - 1 ...

    Text Solution

    |

  10. Assertion (A) : If 1,2,3 are the roots of ax^3 + bx ^2 +cx +d=0 ...

    Text Solution

    |

  11. Assertion (A) : if x^4 -x^3 -6x^2 +4x +8=0 has a multiple root ...

    Text Solution

    |

  12. Assertion (A) : If alpha , beta, gamma are the roots of x^3 -x-...

    Text Solution

    |

  13. Assertion (A ) : the number of roots of x^4 +2x^3 -7x^2 -8x +12=...

    Text Solution

    |

  14. Assertion (A ) : the roots x^4 -5x^2 +6=0 are +- sqrt(2) ,+-sqrt...

    Text Solution

    |

  15. For k gt 0 if k sqrt(-1) is a root of the equation x^4 + 6x^...

    Text Solution

    |

  16. If the roots of the equation x^3 +3px^2 + 3qx -8=0 are in a...

    Text Solution

    |

  17. If the roots of the equation x^(3) - 7x^(2) + 14x - 8 = 0 are in ...

    Text Solution

    |

  18. If alpha , beta , gamma are the roots of x^3 +px^2 +qx +r=0 t...

    Text Solution

    |

  19. If the equation x^5 -3x^4 -5x^3 +27 x^2 - 32 x +12=0 has rep...

    Text Solution

    |

  20. If alpha , beta are the roots of x^2 - 3x +a =0 and gamma ...

    Text Solution

    |