Home
Class 11
MATHS
If x^(2) +ax - 3x-(a+2) = 0 has real and...

If `x^(2) +ax - 3x-(a+2) = 0` has real and distinct roots, then minimum value of `(a^(2)+1)/(a^(2)+2)` is

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise All Questions|363 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

For all real values of x, the minimum value of (1-x+x^(2))/(1+x+x^(2)) is

If x is real number, then the minimum value of x^2+x+1 is

If (a^(2)-14a+13)x^(2)+(a+2)x-2=0 does not have two distinct real roots, then the maximum value of a^(2)-15a is _________.

Let x^2-3x+p=0 has two positive roots aa n db , then minimum value if (4/a+1/b) is,

If a x^2+b x+6=0 does not have distinct real roots, then find the least value of 3a+bdot

If the cubic 2x^3-9x^2+12 x+k=0 has two equal roots then minimum value of |k| is______.

If x_(1) and x_(2) are the real and distinct roots of ax^(2)+bx+c=0 then prove that lim_(xtox1) (1+sin(ax^(2)+bx+c))^(1/(x-x_(1)). equals to

If the root of the equation (a-1)(x^2-x+1)^2=(a+1)(x^4+x^2+1) are real and distinct, then the value of a in a) (-oo,3] b) (-oo,-2)uu(2,oo) c) [-2,2] d) [-3,oo)

If ax^2-bx+c =0 has two distinct roots lying in the interval (0,1),a,b,c in N. Then

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. For x^2-(a+3)|x|+4=0 to have real solutions, the range of a is a. (-oo...

    Text Solution

    |

  2. Find the number of integal values of x satisfying sqrt(-x^2+10x-16)...

    Text Solution

    |

  3. If x^(2) +ax - 3x-(a+2) = 0 has real and distinct roots, then minimum ...

    Text Solution

    |

  4. Let alpha+ibeta;alpha,beta in R , be a root of the equation x^3+q x+r...

    Text Solution

    |

  5. In equation x^4-2x^3+4x^2+6x-21=0 if two its roots are equal in magn...

    Text Solution

    |

  6. If alpha,beta,gamma are the roots of the equation x^3+p x^2+q x+r=0, t...

    Text Solution

    |

  7. The equation x^3+5x^2+px+q=0 and x^3+7x^2+px+r=0 have two roots in com...

    Text Solution

    |

  8. If alpha,beta,gamma are the roots of he euation x^3+4x+1=0, then find ...

    Text Solution

    |

  9. If the roots of the equation x^3+P x^2+Q x-19=0 are each one more that...

    Text Solution

    |

  10. If a ,b ,p ,q are non zero real numbers, then how many comman roots wo...

    Text Solution

    |

  11. If x^2+p x+q=0a n dx^2+q x+p=0,(p!=q) have a common roots, show that 1...

    Text Solution

    |

  12. a,b,c are positive real numbers forming a G.P. If ax^2+2bx+c=0and d...

    Text Solution

    |

  13. If equations x^2+a x+12=0. x^2+b x+15=0a n dx^2+(a+b)x+36=0, have a co...

    Text Solution

    |

  14. If x is real and the roots of the equation a x^2+b x+c=0 are imaginary...

    Text Solution

    |

  15. Solve (x^2+2)^2+8x^2=6x(x^2+2)

    Text Solution

    |

  16. Find the value of 2+1/(2+1/(2+1/(2+oo)))

    Text Solution

    |

  17. If both the roots of a x^2+a x+1=0 are less than 1, then find the exha...

    Text Solution

    |

  18. If both the roots of x^2+a x+2=0 lies in the interval (0, 3), then fin...

    Text Solution

    |

  19. Solve (x^2+3x+2)/(x^2-6x-7)=0.

    Text Solution

    |

  20. Solve sqrt(x-2)+sqrt(4-x)=2.

    Text Solution

    |