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

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

A

0

B

`alphabeta`

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

  • APPLICATIONS OF DERIVATIVES

    TARGET PUBLICATION|Exercise COMPETITIVE THINKING|161 Videos
  • APPLICATIONS OF DERIVATIVES

    TARGET PUBLICATION|Exercise EVALUATION TEST|20 Videos
  • APPLICATIONS OF DERIVATIVES

    TARGET PUBLICATION|Exercise EVALUATION TEST|20 Videos
  • APPICATIONS OF DEFINITE INTEGRAL

    TARGET PUBLICATION|Exercise EVALUATION TEST|18 Videos
  • BINOMIAL DISTRIBUTION

    TARGET PUBLICATION|Exercise EVALUTION TEST|12 Videos

Similar Questions

Explore conceptually related problems

The minimum values of (x-alpha)(x-beta) is

If x^(2)+(a^(2)+100)x-2a=0 (where a in R) has the roots alpha and beta, then minimum value of (1-alpha)(1-beta) is

If the equation x^(2)+(p^(2)+5)x-2p=0(p in R) has roots alpha,beta then find the minimum value of (1-alpha)(1-beta)

Let alpha, beta be any two positive values of x for which 2"cos"x, |"cos"x| " and " 1-3"cos"^(2) x are in G.P. The minimum value of |alpha -beta| , is

If alpha,beta are the roots of the quadratic equation x^(2)-2(1-sin2 theta)x-2cos^(2)(2 theta)=0, then the minimum value of (alpha^(2)+beta^(2)) is equal to

If alpha,beta are the roots of the quadratic equation x^(2)-2(1-sin2 theta)x-2cos^(2)(2 theta)=0, then the minimum value of (alpha^(2)+beta^(2)) is equal to

If alpha & beta are the roots of the quadratic equation x^(2)-(k-2)x-k+1=0 ,then minimum value of alpha^(2)+beta^(2) is

If alpha & beta are the roots of the quadratic equation x^(2)-(k-2)x-k+1=0 , then minimum value of alpha^(2)+beta^(2) is

If alpha and beta are the real roots of the equation x^(2)-(k+1)x-(k+2)=0, then minimum value of alpha^(2)+beta^(2) is

If alpha, beta, gamma are the roots of the equation x^(3)+(a^(4)+4a^(2)+1)x= x^(2)+a^(2) , then the minimum value of Sigma{(alpha)/(beta)+((alpha)/(beta))^(-1)} is equal to

TARGET PUBLICATION-APPLICATIONS OF DERIVATIVES-CRITICAL THINKING
  1. If f(x)=(a sin x+b cosx)/(c sinx+dcosx) is decreasing for all x, then

    Text Solution

    |

  2. It is given that at x=1 , the function x^4-62 x^2+a x+9 attains its ma...

    Text Solution

    |

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

    Text Solution

    |

  4. For the curve y=x e^x , the point

    Text Solution

    |

  5. If f(x)=x^5-5x^4+5x^3-10 has local maximum and minimum at x = p and x ...

    Text Solution

    |

  6. The function y=alogx+b x^2+x has extreme values at x=1 and x=2 . Find ...

    Text Solution

    |

  7. The maximum and minimum values for the funtion f(x)=3x^4-4x^3 on [-1,2...

    Text Solution

    |

  8. The maximum value of function f(x)=x^3-12 x^2+36 x+17 in the interval ...

    Text Solution

    |

  9. If x + y = 16 and x^2 + y^2 is minimum, then the values of x and y are

    Text Solution

    |

  10. The maximum value of f(x)=(x-1)^(1/2)(x-2),1lexle9,is

    Text Solution

    |

  11. The function xsqrt(1-x^(2)),(x gt0) has

    Text Solution

    |

  12. The sum of two natural numbers is 10. Their product is maximum if the ...

    Text Solution

    |

  13. Maximum area of a rectangle whose perimeter is given as 24 metres is ...

    Text Solution

    |

  14. If sum of two numbers is 3, then maximum value of the product of first...

    Text Solution

    |

  15. The two parts of 100 for which the sum of double of first and square o...

    Text Solution

    |

  16. The adjacent sides of a rectangle with given perimeter as 100 cm and e...

    Text Solution

    |

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

    Text Solution

    |

  18. x^(2x) has a stationary point at

    Text Solution

    |

  19. What is the maximum value o fx y subject to the condition x+y=8 ?

    Text Solution

    |

  20. If f(x)=2x^(3)-21x^(2)+36x-30, then which one of the following is corr...

    Text Solution

    |