Home
Class 12
MATHS
If x ,y ,a n dz are real and different a...

If `x ,y ,a n dz` are real and different and `u=x^2+4y^2+9z^2-6y z-3z x-2x y ,t h e nu` is always a. non-negative b. zero c. non-positive d. none of these

A

non-negative

B

non-positive

C

zero

D

none of these.

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • Ellipse and Hyberbola

    A DAS GUPTA|Exercise EXERCISE|65 Videos
  • Function

    A DAS GUPTA|Exercise Exercise|57 Videos

Similar Questions

Explore conceptually related problems

If x,y, and z are real and different and u=x^(2)+4y^(2)+9z^(2)-6yz-3zx-2xy, then u is always a.non-negative b.zero c.non-positive d.none of these

If x, y and z are real and distinct, then x^(2)+9y^(2)+16z^(2)-3xy-12yz-4zx is always

If x,y,z are real and 4x^(2)+9y^(2)+16z^(2)=2xyz{(6)/(x)+(4)/(y)+(3)/(z)}

The least value of the expression x^(2)+4y^(2)+3z^(2)-2x-12y-6z+14 is a.1 b.no least value c.0 d.none of these

If x.y,z are positive real numbers such that x^(2)+y^(2)+z^(2)=27, then x^(3)+y^(3)+z^(3) has

If x,y and z are three real numbers such that x+y+z=4 and x^(2)+y^(2)+z^(2)=6, then show that each of x,y and z lie in the closed interval [(2)/(3),2]

A DAS GUPTA-Equations, Inequation and Expressions-Exercise
  1. The real value of a for which x^2+i(a-1)x+5=0 will have a pair of con...

    Text Solution

    |

  2. If a, b, c are positive then both roots of the equation ax^2 + bx+c=0

    Text Solution

    |

  3. The expression a^2x^2+bx+1 will be positive for all x in R if

    Text Solution

    |

  4. If x ,y ,a n dz are real and different and u=x^2+4y^2+9z^2-6y z-3z x-2...

    Text Solution

    |

  5. The least value of ax^2+bx+c,(a>0) is

    Text Solution

    |

  6. If x be real, then the maximum value of 5+4x-4x^2 will be equal to

    Text Solution

    |

  7. If x^2+p x=1 is a factor of the expression a x^3+b x=c , then a^2-c^2=...

    Text Solution

    |

  8. If a+b+c=0, then, the equation 3ax^(2)+2bx+c=0 has , in the interval ...

    Text Solution

    |

  9. If the value of ax^2+bx+c is always an integer for integral values of ...

    Text Solution

    |

  10. If a gt 1 , then the roots of the equation (1-a)x^(2)+3ax-1=0 are

    Text Solution

    |

  11. Fill in the blank : If f(x) = x+1/x , x in R Then the set of possible ...

    Text Solution

    |

  12. Fill in the blank : If 1+ i is a root of the equation ix^2-3x+p = 0 wh...

    Text Solution

    |

  13. Equation cos 2x+7=a(2-sin x) can have a real solution for

    Text Solution

    |

  14. If alpha,beta be the roots of x^2 - x-1 = 0 and An = alpha^n +beta^n, ...

    Text Solution

    |

  15. For all lambda in R, The equation ax^2+ (b - lambda)x + (a-b-lambda)= ...

    Text Solution

    |

  16. Prove that (a^2 + b^2) x^2 - 2b(a+c)x + (b^2+ c^2) ge 0 for all x in R...

    Text Solution

    |

  17. Let f(x)= x^4- 3x^3 + 2x^2-3x+ a.If f(sqrt-1)= 0 and a in R then prove...

    Text Solution

    |

  18. If a1x^3 + b1x² + c1x + d1 = 0 and a2x^3 + b2x^2+ c2x + d2 = 0 have a ...

    Text Solution

    |

  19. Find all numbers p for each of which the least value of the quadratic ...

    Text Solution

    |

  20. Prove that the equation x^3 + 2x^2 +x + 4 = 0 has exactly one root in ...

    Text Solution

    |