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

A

`log_5abc=1`

B

`log_6abc=2`

C

`log_5abc=3`

D

`log_6abc=4`

Text Solution

Verified by Experts

The correct Answer is:
B, C, D
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. The equation (x/(x+1))^2+(x/(x-1))^2=a(a-1) has

    Text Solution

    |

  2. If alpha and beta are roots of the equation ax^2+bx+c=0 and, if px^2+q...

    Text Solution

    |

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

    Text Solution

    |

  4. If ax^2+bx+c=0 and cx^2+bx+a=0 (a,b,cinR) have a common non-real roots...

    Text Solution

    |

  5. LetP(x)=0 be the polynomial equation of least possible degree with rat...

    Text Solution

    |

  6. If 2a+3b+6c=0(a,b,cinR), then the quadratic equation ax^2+bx+c=0 has

    Text Solution

    |

  7. If (alpha,beta)∈ R are two of an quadratic equations,then the equation...

    Text Solution

    |

  8. If a,binR are two of an quadratic equations,then the equation will be ...

    Text Solution

    |

  9. Letf(x)=x^2+b1x+c1,g(x)=x^2+b2x+c2. Real roots fo f(x)=0 be alpha,beta...

    Text Solution

    |

  10. Letf(x)=x^2+b1x+c1,g(x)=x^2+b2x+c2. Real roots fo f(x)=0 be alpha,beta...

    Text Solution

    |

  11. match list i with list ii

    Text Solution

    |

  12. match the equation on left with the properties on right

    Text Solution

    |

  13. If the quadratic polynomial, y=(cot alpha)x^2+2(sqrtalpha)x+1/2tanalph...

    Text Solution

    |

  14. If alpha,beta be the roots x^2+px-q=0 and gamma,delta be the roots of ...

    Text Solution

    |

  15. The smallest value of k, for which both roots of the equation x^2-8kx+...

    Text Solution

    |

  16. Let (x,y,z) be points with Integer coordinates satisfying the system o...

    Text Solution

    |

  17. If roots of the equation x^2-10cx-11d=0 are a,b and those of x^2-10ax-...

    Text Solution

    |

  18. If alpha,beta,gamma are such that alpha+beta+gamma=4, alpha^2+beta^2+g...

    Text Solution

    |

  19. Find the values of the parameter a for which the roots of the quadrati...

    Text Solution

    |

  20. Find the values of the parameter a for which the roots of the quadrati...

    Text Solution

    |