Home
Class 12
MATHS
The minimum value of (x- alpha)(x-beta) ...

The minimum value of `(x- alpha)(x-beta)` is

A

0

B

`alpha beta`

C

`1/4(alpha - beta)^(2)`

D

`-1/4(alpha - beta)^(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
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

The minimum value of x^(x) is

If alpha, beta the roots of 8x^(2) - 3x + 27 = 0 , then the value of [ ( (alpha^(2))/(beta))^(1//3) + ((beta^(2))/(alpha))^(1//3) ] is ,

If alpha and beta are the zeroes of the polynomial 2x^2 + 5x + 1 , then the value of alpha +beta+ alpha beta is

If alpha and beta are zeros of f(x) = 6x^(2) + x= 2 find the value fo (alpha)/(beta) +(beta)/(alpha) .

If alpha,beta and gamma are roots of x^(3) -2x+1=0,then the value of Sigma((1)/(alpha+beta-gamma)) is

If alpha and beta are the zeroes of the polynomial f(x) = 3x^(2)+5x+7 then find the value of (1)/(alpha^(2))+(1)/(beta^(2)) .

If alpha,beta,gamma are the roots of x^3-x^2-1=0 then the value of (1+alpha)/(1-alpha)+(1+beta)/(1-beta)+(1+gamma)/(1-gamma) is equal to

If alpha,beta be the roots of the equation 3x^2+2x+1=0, then find value of ((1-alpha)/(1+alpha))^3+((1-beta)/(1+beta))^3

If alpha, beta, and gamma are the zeros of 2x^(3) - 4x^(2) + 6x +9 , find value of alpha ^(-1) + beta^(-1) + gamma^(-1)

HIMALAYA PUBLICATION-MAXIMA AND MINIMA-QUESTION BANK
  1. The minimum value of x^(x) is

    Text Solution

    |

  2. The maximum value of xy subjects to x+y =7 is

    Text Solution

    |

  3. The minimum value of (x- alpha)(x-beta) is

    Text Solution

    |

  4. Show that y = log(1 +x) - (2x)/(2 + 2x) , x gt -1, is an increasing fu...

    Text Solution

    |

  5. The function f(x) = xe^(-x) (x in R) attains a maximum value at x =

    Text Solution

    |

  6. Observe the following statements: A : f(x) = 2x^(3)-9x^(2)+12x-3 is in...

    Text Solution

    |

  7. If x is real then the minimum value of (x^(2)-x+1)/(x^(2)+x+1) is

    Text Solution

    |

  8. The perimeter of a sector is a constant . If its area is to be maximum...

    Text Solution

    |

  9. In the interval (-3,3) the function f(x) = x/3 + 3/x, x ne 0 is

    Text Solution

    |

  10. The function f(x) = 1-x^(3)-x^(5) is decreasing for

    Text Solution

    |

  11. If PQ and PR are the two sides of a triangle, then the angle between t...

    Text Solution

    |

  12. The function y = a(1-cosx) is maximum when x is equal to

    Text Solution

    |

  13. Twenty metres are available to fence a flower bed in the form of a cir...

    Text Solution

    |

  14. The function f(x) = tan^(-1) (sin x + cos x), x gt 0 is always an incr...

    Text Solution

    |

  15. The maximum value of xy, when x+2y = 8 is

    Text Solution

    |

  16. The denominator of a fraction is greater them 16 of the square of nume...

    Text Solution

    |

  17. If xy = c^(2), then minimum value of ax + by is

    Text Solution

    |

  18. If a^(2)x^(4) + b^(2)y^(4) = c^(6), then maximum value of xy is

    Text Solution

    |

  19. If f(x) = 1/(4x^(2)+2x+1), then its maximum value

    Text Solution

    |

  20. Let f(x)=(x)/(1+x)-log(1+x), when x gt 0, then f is :

    Text Solution

    |