Home
Class 12
MATHS
Let a,b and c be three distinct real roo...

Let a,b and c be three distinct real roots of the cubic `x ^(3) +2x ^(2)-4x-4=0.` If the equation `x ^(3) +qx ^(2)+rx+le =0` has roots `1/a, 1/b and 1/c,` then the vlaue of `(q+r+s)` is equal to :

A

`3/4`

B

`1/2`

C

`1/4`

D

`1/6`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

    VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|44 Videos

  • QUADRATIC EQUATIONS

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

  • PROBABILITY

    VIKAS GUPTA (BLACK BOOK)|Exercise Exercise -5 : Subjective Type problems|12 Videos

  • SEQUENCE AND SERIES

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

Similar Questions

Explore conceptually related problems

Let a and b be two distinct roots of the equation x^(3)+3x^(2)-1=0 The equation which has (ab) as its root is

The number of distinct real roots of x^(4)-4x^(3)+12x^(2)+x-1=0

Number of distinct real roots of equation 3x^4+4x^3-12x^2+4=0

The number of distinct real roots of x^(4)-4x^(3)+12x^(2)+x-1=0 is :

If the equation x^(4)+px^(3)+qx^(2)+rx+5=0 has four positive real roots, find the maximum value of pr .

The number of distinct real roots of the equation 3x^(4)+4x^(3)-12x^(2)+4=0 is ___________.

If the equation x^(5) - 10 a^(3)x^(2) + b^(4)x + c ^(5) = 0 has three equal roots, then

Given a,b, c are three distinct real numbers satisfying the inequality a-2b+4c gt0 and the equation ax ^(2) + bx +c =0 has no real roots. Then the possible value (s) of (4a +2b+x)/(a+3b+9c) is/are:

The roots of the equation x^(2)+px+q=0 are 1 and 2 .The roots of the equation qx^(2)-px+1=0 will be

VIKAS GUPTA (BLACK BOOK)-QUADRATIC EQUATIONS -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. Let a,b and c be three distinct real roots of the cubic x ^(3) +2x ^(2...

    Text Solution

    |

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

    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, wher...

    Text Solution

    |

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

    Text Solution

    |

  6. If the equatio (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 +17x+71 is perfect square of a ...

    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 the roots of the equation, x^2...

    Text Solution

    |

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

    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) be a polynomial equation of least possible degree, with rati...

    Text Solution

    |

  21. The range of values k for which the equation 2 cos ^(4)x-sin ^(4)x +k=...

    Text Solution

    |