Home
Class 12
MATHS
If the equation x^(4)+px^(3)+qx^(2)+rx+5...

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

Promotional Banner

Topper's Solved these Questions

  • SEQUENCE & SERIES

    MOTION|Exercise Exercise -1 Objective Problems /JEE Main Section -A : AP|24 Videos

  • SEQUENCE & SERIES

    MOTION|Exercise Exercise -2 (Level -I) Objective Problems /JEE Main AP|23 Videos

  • QUADRATIC EQUATION

    MOTION|Exercise EXERCISE 4 (PREVIOUS YEAR| JEE MAIN)|25 Videos

  • SOLUTION OF TRIANGLE

    MOTION|Exercise EXERCISE - 4( LEVEL II)|10 Videos

Similar Questions

Explore conceptually related problems

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

if the equation x^(4)-4x^(3)+ax^(2)+bx+1=0 has four positive roots, then find a.

If x^4+px^3+qx^2+rx+5=0 has four positive roots,then the minimum value of pr is equal to

The equation 2x ^(3) -3x ^(2) +p=0 has three real roots. Then find the minimum value of p.

if the roots of the cubic x^(3)-12x^(2)+ax-64=0 are positive real numbers, then find the minimum value of a

If -4 is a root of the equation x^(2)+px-4=0 and the equation x^(2)+px+q=0 has coincident roots, find the values of p and q.

Given that 2 is a root of the equation 3x^(2)-p(x+1)=0 and that the equation px^(2)-qx+9=0 has equal roots,find the values of p and q

If one root of the equation x^(2)+px+12=0 is 4, while the equation x^(2)+px+q=0 has equal roots,then find the value of q.

MOTION-SEQUENCE & SERIES -Exercise -4 Level -II Previous Year /JEE Advanced
  1. If the equation x^(4)+px^(3)+qx^(2)+rx+5=0 has four positive real root...

    Text Solution

    |

  2. Let Vr denote the sum of first r terms of an arithmetic progression (A...

    Text Solution

    |

  3. Let Vr denote the sum of the first r terms of an arithmetic progressio...

    Text Solution

    |

  4. Let Vr denote the sum of the first r terms of an arithmetic progressio...

    Text Solution

    |

  5. Let A1 , G1, H1denote the arithmetic, geometric and harmonic means re...

    Text Solution

    |

  6. Let A1 , G1, H1denote the arithmetic, geometric and harmonic means re...

    Text Solution

    |

  7. Let A1 , G1, H1denote the arithmetic, geometric and harmonic means re...

    Text Solution

    |

  8. A straight line through the vertex P of a triangle PQR intersects the ...

    Text Solution

    |

  9. Suppose four distinct positive numbers a1,a2,a3,a4 are in G.P. Let b1=...

    Text Solution

    |

  10. In the sum of first n terms of an A.P. is cn^2, then the sum of square...

    Text Solution

    |

  11. Let Sk ,k=1,2, ,100 , denotes thesum of the infinite geometric series ...

    Text Solution

    |

  12. Let a(1),a(2),a(3),"........."a(11) be real numbers satisfying a(1)=15...

    Text Solution

    |

  13. The minimum value of the sum of real number a^(-5),a^(-4),3a^(-3),1,a^...

    Text Solution

    |

  14. Let a1, a2, a3, ,a(100) be an arithmetic progression with a1=3a n dsp...

    Text Solution

    |

  15. If a(1),a(2),a(3),"......" be in harmonic progression with a(1)=5 and ...

    Text Solution

    |

  16. Let a(n) denote the number of all n-digit numbers formed by the digits...

    Text Solution

    |

  17. Let an denote the number of all n-digit positive integers formed by th...

    Text Solution

    |

  18. Let S(n)=sum(k=1)^(4n)(-1)^((k(k+1))/2)k^(2). Then S(n) can take value...

    Text Solution

    |

  19. A pack contains n cards numbered from 1 to n. Two consecutive numbered...

    Text Solution

    |

  20. Let a,b,c be positive integers such that (b)/(a) is an integer. If a,b...

    Text Solution

    |

  21. Suppose that all the terms of an arithmetic progression (A.P.) are nat...

    Text Solution

    |