Home
Class 12
MATHS
The cubic polynomial with leading coeffi...

The cubic polynomial with leading coefficient unity all whose roots are 3 units less than the roots of the equation `x ^(3) -3x ^(2) -4x +12=0` is denoted as `f (x) ` then `f '(x)` is equal to :

A

`3x ^(2) -12x +5`

B

`3x ^(2) +12x+5

C

`3x ^(2) +12x -5`

D

`3x ^(2) -12x -5`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|42 Videos

  • QUADRATIC EQUATIONS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|23 Videos

  • PROBABILITY

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise -5 : Subjective Type problems|11 Videos

  • SEQUENCE AND SERIES

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|21 Videos

Similar Questions

Explore conceptually related problems

Find the equation of whose roots is greater by unity than the roots of the equation x^3-5x^2+6x-3=0

Find the equation whose roots are (1)/(4) times of the roots of the equation x^(2)-3x+2=0

Find the polynomial equation whose roots are the negatives of the roots of the equation x^4 -6x +7x^2 -2x +1=0

Find the cubic equation whose roots are the squares of the roots of the equation x^3 +p_1 x^2 +p_2 x+p_3 =0

Find the number of real roots of the equation f(x) =x^(3) + 2x^(2) +x +2 =0

If for all real values of a one root of the equation x^2-3ax + f(a)=0 is double of the other, then f(x) is equal to

Find the polynomial equation whose roots are the translates of the roots of the equation . x^4-x^3-10x^2+4x+24=0 by 2 .

If one the roots fo the equation x^(2) +x f(a) + a=0 is the cube of the othere for all x in R , then f(x)=

Find the transformed equation whose roots are the negatives of the roots of the equation x^4 +5x^3 +11 x+3=0

Find the equation whose roots are 3 times the roots of x^3 +2x^2 -4x +1=0

VIKAS GUPTA (BLACK BOOK) ENGLISH-QUADRATIC EQUATIONS -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. The cubic polynomial with leading coefficient unity all whose roots ar...

    Text Solution

    |

  2. Let f (x) =ax ^(2) + bx+ c where a,b,c are integers. If sin ""pi/7. si...

    Text Solution

    |

  3. Let a, b, c, d be distinct integers such that the equation (x - a) (x ...

    Text Solution

    |

  4. Consider the equation (x^2 + x + 1)^2-(m-3)(x^2 + x + 1) +m=0--(1), w...

    Text Solution

    |

  5. The number of positive integral values of , m le 16 for which the equa...

    Text Solution

    |

  6. If the equation (m^(2) -12 )x^(4) -8x ^(2)-4=0 has no real roots, then...

    Text Solution

    |

  7. The least positive integral value of 'x' satisfying (e^x-2)(sin(x+pi/...

    Text Solution

    |

  8. The integral values of x for which x ^(2) + 17 x +7 is perfect square ...

    Text Solution

    |

  9. Let p(x) =x^6-x^5-x^3-x^2-x and alpha, beta, gamma, delta are the root...

    Text Solution

    |

  10. The number of real values of 'a' for which the largest value of the fu...

    Text Solution

    |

  11. The number of all values of n, (whre n is a whole number ) for which t...

    Text Solution

    |

  12. The number of negative intergral values of m for which the expression ...

    Text Solution

    |

  13. If the expression a x^4+b x^3-x^2+2x+3 has remainder 4x+3 when divided...

    Text Solution

    |

  14. The smallest value of k for which both roots of the equation x^(2)-8kx...

    Text Solution

    |

  15. If x ^(2) -3x+2 is a factor of x ^(4) -px ^(2) +q=0, then p+q=

    Text Solution

    |

  16. The expression x^2 + 2xy + ky^2 + 2x + k = 0 can be resolved into two ...

    Text Solution

    |

  17. The curve y=(lambda=1)x^2+2 intersects the curve y=lambdax+3 in exactl...

    Text Solution

    |

  18. Find the number of integral vaues of 'a' for which the range of functi...

    Text Solution

    |

  19. When x ^(100) is divided by x ^(2) -3x +2, the remainder is (2 ^(k +1)...

    Text Solution

    |

  20. Let p(x)=0 be a polynomial equation of the least possible degree, with...

    Text Solution

    |

  21. The range of value's of k for which the equation 2 cos^(4) x - sin^(4...

    Text Solution

    |