Home
Class 11
MATHS
Ifax^2-bx+c=0 has two distinct roots lyi...

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

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

The number of values of k for which the equation x^(2)-3x+k=0 has two distinct roots lying in the interval ( 0 , 1 ) are

The number of values of k for which the equation x^3-3x+k=0 has two distinct roots lying in the interval (0,1) is (a) three (b) two (c) infinitely many (d) zero

Find the value of a which the equation 4x^2-2x+a =0 has two roots lying in the interval (-1,1)

The necessary and sufficient condition for the equation (1-a^2)x^2+2ax-1 =0 to have roots lying in the interval (0,1) is

If 2a+3b+6c=0 then the equation ax^2+bx+c=0 has in the interval (0,1)

If a , b , c are positive numbers such that a gt b gt c and the equation (a+b-2c)x^(2)+(b+c-2a)x+(c+a-2b)=0 has a root in the interval (-1,0) , then

Let a,b,c be real. If ax^2+bx+c=0 has two real roots alpha,beta where alphalt-1 and betagt 1 ,then show that 1+c/a+abs(b/a)lt0 .

If ax^(2)+bx+c=0 , a ne 0 , a , b , c in R has distinct real roots in (1,2) , then a and 5a+2b+c have (a) same sign (b) opposite sign (c) not determined (d) none of these

The equation x^(2)+bx+c=0 has distinct roots. If 2 is subtracted from each root the result are the reciprocal of the original roots, then b^(2)+c^(2) is

if ax^2+bx+c = 0 has imaginary roots and a+c lt b then prove that 4a+c lt 2b

PATHFINDER-QUADRATIC EQUATION AND EXPRESSION-QUESTION BANK
  1. Find values of a for which the quadratic equation 3x^2+2(a^2+1)x+(a^2-...

    Text Solution

    |

  2. For what real 'p' do the roots of x^2-2x-p^2+1=0 lie between the roots...

    Text Solution

    |

  3. Ifax^2-bx+c=0 has two distinct roots lying in the interval (0,1),a,b,c...

    Text Solution

    |

  4. Find the values of theta in the interval (-pi/2,pi/2) satisfying the e...

    Text Solution

    |

  5. Find the value of lamda for which the inequality 3-abs(x-lamda)gtx^2 i...

    Text Solution

    |

  6. The equation x-2/(x-1)=1-2/(x-1) has

    Text Solution

    |

  7. Let alpha,beta be the equation x^2-px+r=0 and alpha/2,2beta be the roo...

    Text Solution

    |

  8. If alpha,beta,gamma are the roots of the equation x^3+x+1=0, then the ...

    Text Solution

    |

  9. alpha,beta are the roots of the equation (a-2)x^2-(5-a)x-5=0.Find 'a' ...

    Text Solution

    |

  10. If f(x) = g(x)^3+xh(x)^3 is divisible by x^2+x+1, then

    Text Solution

    |

  11. If the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal,the...

    Text Solution

    |

  12. If the roots of the equation 6x^3-11x^2+6x-1=0 are in H.P., then the r...

    Text Solution

    |

  13. A value of b for which the equations x^2+bx-1=0, x^2+x+b =0 have one r...

    Text Solution

    |

  14. If a,b,c are in G.P., then the equations ax^2+2bx+c =0 and dx^2+2ex+f ...

    Text Solution

    |

  15. In what interval 'm' must lie so that the root of the equation x^2-2mx...

    Text Solution

    |

  16. The necessary and sufficient condition for the equation (1-a^2)x^2+2ax...

    Text Solution

    |

  17. For all 'x', x^2+2ax+(10-3a)gt0, then the interval .In which 'a' lies ...

    Text Solution

    |

  18. The maximum value of 2-3x-4x^2

    Text Solution

    |

  19. Number of solution of equation sin^(-1)x+cos^(-1)(x^2)=pi/2

    Text Solution

    |

  20. The equation sqrt(x+1)-sqrt(x-1)=sqrt(4x-1) has

    Text Solution

    |