Home
Class 11
MATHS
If the roots of x^2+bx+c=0 are both real...

If the roots of `x^2+bx+c`=0 are both real and greater than unity, then (b+c+1)

A

may be less than zero

B

may be equal to zero

C

must be greater than zero

D

must be less than zero

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATION

    PATHFINDER|Exercise QUESTION BANK|19 Videos
  • RECTANGULAR CO-ORDINATES

    PATHFINDER|Exercise QUESTION BANK|27 Videos

Similar Questions

Explore conceptually related problems

If roots of x^2-(a-3)x+a =0 are such that both of them is greater than 2, then

If both the roots of x^2-a x+a=0 are greater than 2, then find the value of adot

If roots of equation x^2-2c x+a b=0 are real and unequal, then prove that the roots of x^2-2(a+b)x+a^2+b^2+2c^2=0 will be imaginary.

Prove that the roots of ax^2+2bx+c=0 will be real and distinct if and only if the roots of (a+c) (ax^2+2bx+c) =2 (ac-b^2) (x^2+1) are imaginary

If the two roots of the equation ax^2 + bx + c = 0 are distinct and real then

If the roots of x^2-bx+c=0 be two consecutive integers, then the value of b^2-4c will be-

All the values of m for whilch both the roots of the equation x^2-2m x+m^2-1=0 are greater than -2 but less than 4 lie in the interval A -2 B. m >3 C. -1ltmlt3 D. 1ltmlt4

Let a >0,b >0 and c >0 . Then, both the roots of the equation a x^2+b x+c=0 : a. are real and negative b. have negative real parts c. have positive real parts d. None of the above

IF a=0, bne0 and c is real and rational then one root of the equation ax^2+bx+c=0 is real and rational and the other root is -

If one root of the equation x^2+bx+8=0 be 4 and the roots of the equation x^2+bx+c=0 are equal , find the value of c.

PATHFINDER-QUADRATIC EQUATION AND EXPRESSION-QUESTION BANK
  1. The harmonic mean of the roots of the equation (5+sqrt)x^2-(4+sqrt5)x+...

    Text Solution

    |

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

    Text Solution

    |

  3. If the roots of x^2+bx+c=0 are both real and greater than unity, then ...

    Text Solution

    |

  4. Value of p, so that 6 lies between roots of the equation x^2+2(p-3)x+9...

    Text Solution

    |

  5. Ifx^2-(a-3)x+a=0 has at least one positive root,then

    Text Solution

    |

  6. If the roots of the equation x^2-2ax+a^2 + a-3=0 are less than 3 then

    Text Solution

    |

  7. The number of solutions of log2(x-1)=2log2(x-3) is

    Text Solution

    |

  8. If x=(sqrt13+2sqrt3), then x+1/x is equal to ?

    Text Solution

    |

  9. The sum of all real roots of the equationabs(x-2)^2+abs(x-2)-2=0 is

    Text Solution

    |

  10. If alpha is a root of 4x^2+2x-1=0, then the other root is

    Text Solution

    |

  11. If e^(cos x)-e^(-cos x) =4, then the value of the cosx is

    Text Solution

    |

  12. If altbltcltd, then the roots of equation (x-a)(x-c)+2(x-b)(x-d)=0, ar...

    Text Solution

    |

  13. If alphaand beta(alphaltbeta) are the roots of the equation x^2+bx+c=0...

    Text Solution

    |

  14. If tan of angles A,B,C are the solutions of the equations tan^3x+3ktan...

    Text Solution

    |

  15. The number of solutions of the equation sin(e^x)=5^x+5^(-x)is

    Text Solution

    |

  16. If p(x) be a polynomial satisfying the identity p(x^2)+2x^2+10x=2xp(x+...

    Text Solution

    |

  17. Ifbgta, then the equation (x-a)(x-b)-1=0, has

    Text Solution

    |

  18. The value of alpha and beta such that equation x^2+2x+2+e^a-sinbeta=0 ...

    Text Solution

    |

  19. The values of 'a' for which x^2+ax+sin^-1(x^2-4x+5)+cos^-1(x^2-4x+5)=...

    Text Solution

    |

  20. The number of real solution to the equation -x^2+x-1=sin^(2)x

    Text Solution

    |