Home
Class 11
MATHS
Find the value of a for which the sum of...

Find the value of `a` for which the sum of the squares of the roots of the equation `x^2-(a-2)x-a-1=0 ` assumes the least value.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise All Questions|365 Videos

  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

Similar Questions

Explore conceptually related problems

The value of a so that the sum of the squares of roots of the equation x^2-(a-2)x-a+1=0 assume the least value is

The value of 'p' for which the sum of the square of the roots of 2x^2-2(p-2)x-p-1=0 is least, is

The value of k for which the sum of the squares of the roots of 2x^(2)-2(k-2)x-k=0 is least is

Find the value of m for which the sum of the roots of the equation 5x^2-4x+2+m(4x^2-2x-1)=0 is 6.

Find the sum of and product of the roots of the equation 3x ^2 +2x -1=0 .

The least value of |a| for which tan theta and cot theta are the roots of the equation x^(2)+ax+b=0

The square of sum of the roots of the equation x^(3)+2x^(2)+2x+1=0 equals to

The square of sum of the roots of the equation x^(3)+2x^(2)+2x+1=0 equals to

If the roots of the equation x^(2)-4x-log_3 a=0 , are real , the least value of a is :

The value of a for which twice the sum of the cubes of the roots of the equation a=(x^(2)-3)/(x-2) attains its minimum value is (where, a in[0, pi] )

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If a+b+c=0 then check the nature of roots of the equation 4a x^2+3b x+...

    Text Solution

    |

  2. The complex numbers z1, z2 and z3 satisfying (z1-z3)/(z2-z3) =(1- i sq...

    Text Solution

    |

  3. Find the value of a for which the sum of the squares of the roots of t...

    Text Solution

    |

  4. For all complex numbers z1,z2 satisfying |z1|=12 and |z2-3-4i|=5, fin...

    Text Solution

    |

  5. If x1, a n dx2 are the roots of x^2+(sintheta-1)x-1/2(cos^2theta)=0, ...

    Text Solution

    |

  6. If y="sec"(tan^(-1)x),t h e n(dy)/(dx)a tx=1 is (a)cospi/4 (b) sinp...

    Text Solution

    |

  7. If p ,q in {1,2,3,4,5} , then find the number of equations of form p^2...

    Text Solution

    |

  8. If a^2+b^2=1 t h e n (1+b+i a)/(1+b-i a)= 1 b. 2 c. b+i a d. a+...

    Text Solution

    |

  9. Find the domain and the range of f(x)=sqrt(x^2-3x.)

    Text Solution

    |

  10. Show that the equation Z^4+2Z^3+3Z^2+4Z+5=0 has no root which is eithe...

    Text Solution

    |

  11. Find the domain and range of f(x)=sqrt(3-2x-x^2)

    Text Solution

    |

  12. If x in (0,pi//2)a n dcosx=1//3 , then prove that sum(n=0)^oo(cosn x)/...

    Text Solution

    |

  13. Prove that if the equation x^2+9y^2-4x+3=0 is satisfied for real value...

    Text Solution

    |

  14. Let Zp=rp(costhetap+isinthetap),p=1,2,3a n d1/(Z1)+1/(Z2)+1/(Z3)=0. Co...

    Text Solution

    |

  15. Find the least value of ((6x^2-22 x+21))/((5x^2-18x+17)) for real xdot

    Text Solution

    |

  16. Let a ,b and c be any three nonzero complex number. If |z|=1 and' z ' ...

    Text Solution

    |

  17. Find the range of the function f(x)=x^2-2x-4.

    Text Solution

    |

  18. If x=9^(1/3) 9^(1/9) 9^(1/27) ...->∞ , y= 4^(1/3) 4^(-1/9) 4^(1/27) ....

    Text Solution

    |

  19. Find the linear factors of 2x^2-y^2-x+x y+2y-1.

    Text Solution

    |

  20. If a<0,b>0, then sqrt(a)sqrt(b) is equal to (a)-sqrt(|a|b) (b...

    Text Solution

    |