Home
Class 12
MATHS
Suppose the cubic x^(3)-px+q has three d...

Suppose the cubic `x^(3)-px+q` has three distinct real roots, where `p gt 0` and `q gt 0`. Then which one of the following holds ?

A

The cubic has minimum at both `sqrt(p/3)` and `-sqrt(p/3)`

B

The cubic has maximum at both `sqrt(p/3)` and `-sqrt(p/3)`

C

The cubic has minimum at `sqrt(p/3)`, maximum at `-sqrt(p/3)`

D

The cubic has minimum at `-sqrt(p/3)`, maximum at `sqrt(p/3)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • MATRICES AND DETERMINANTS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|367 Videos

  • MEASUREMENT OF ANGLES, TRIGONOMETRIC RATIOS AND RELATION BETWEEN SIDES AND ANGLES OF A TRIANGLE

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|251 Videos

Similar Questions

Explore conceptually related problems

If x^(2)-p x+q=0 has equal integral roots, then

x and b are real numbers. If b gt 0 and |x| gt b , then

Consider the equation of the parabola y^(2)+4ax=0 where a gt0 which of the following is false

The equation (cosp - 1)x^(2) + (cosp)x + sinp = 0 , where x is a variable, has real roots. Then the interval of p may be any one of the following :

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

The real number k for which the equation : 2x^(3)+3x+k=0 has two distinct real roots in [0, 1] :

If f(x) is a cubic polynomial x^3 + ax^2+ bx + c such that f(x)=0 has three distinct integral roots and f(g(x)) = 0 does not have real roots, where g(x) = x^2 + 2x - 5, the minimum value of a + b + c is

Let a in R and f : R rarr R be given by f(x)=x^(5)-5x+a , then (a) f(x)=0 has three real roots if a gt 4 (b) f(x)=0 has only one real root if a gt 4 (c) f(x)=0 has three real roots if a lt -4 (d) f(x)=0 has three real roots if -4 lt a lt 4

If the equation x^(2)-2px+q=0 has two equal roots, then the equation (1+y)x^(2)-2(p+y)x+(q+y)=0 will have its roots real and distinct only, when y is negative and p is not unity.

HIMALAYA PUBLICATION-MAXIMA AND MINIMA-QUESTION BANK
  1. If f: R rarr R is defined by f(x)=(x)/(x^(2)+1) find f(f(2))

    Text Solution

    |

  2. The function f(x)=tan^(-1)(sinx+cosx) is an increasing function in :

    Text Solution

    |

  3. Suppose the cubic x^(3)-px+q has three distinct real roots, where p gt...

    Text Solution

    |

  4. The condition f(x) = x^(3)+px^(2)+qx+r (x in R) to have no extreme val...

    Text Solution

    |

  5. If m and M respectively the minimum and maximum of f(x)=(x-1)^(2)+3 fo...

    Text Solution

    |

  6. Let, f(x) = int0^(x) (cos t)/t dt. Then x = (2n+1) pi/2, f(x) has

    Text Solution

    |

  7. The point of extremum of the function phi (x) = int1^(x) e^(t^(2)/2) (...

    Text Solution

    |

  8. If f'(x)=(x-a)^(2n)(x-b)^(2p+1), when n and p are positive integers, t...

    Text Solution

    |

  9. If f(x) = kx^(3) - 9x^(2) +9x + 3 is increasing on R then

    Text Solution

    |

  10. If h(x) = f(x) + f(-x) then h(x) has got an extreme value at a point w...

    Text Solution

    |

  11. If a lt 0, the function f(x)=e^(ax)+e^(-ax) is decreasing for all valu...

    Text Solution

    |

  12. If a lt 0, f(x) = e^(ax) + e^(-ax) and S = {x: f(x) is monotonically ...

    Text Solution

    |

  13. If y = a logx + bx^(2) + x has its extremum value at x = -1 and x = 2,...

    Text Solution

    |

  14. f(x) = ((e^(2x)-1)/(e^(2x)+1)) is

    Text Solution

    |

  15. If f(x) = 2x^(3)-21x^(2)+36x-30, then for f(x) which one of the follow...

    Text Solution

    |

  16. The value of k in order that f(x)=sin x-cos x-kx +b decrease for all r...

    Text Solution

    |

  17. The maximum area of a rectangle that can be inscribed in a circle of r...

    Text Solution

    |

  18. The maximum value of (logx)/(x) in (2,oo) is

    Text Solution

    |

  19. The minimum value of 26^(cos 2x) 81 ^(sin 2x) is

    Text Solution

    |

  20. A wire of lenggth 20 cm is bent in the form of a sector of a circle. T...

    Text Solution

    |