Home
Class 11
MATHS
If 2a+3b+6c=0, then prove that at least ...

If `2a+3b+6c=0,` then prove that at least one root of the equation `a x^2+b x+c=0` lies in the interval (0,1).

A

(0,1)

B

(1,2)

C

(2,3)

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • MEAN VALUE THEOREMS

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|4 Videos

  • MATRICES

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos

  • PAIR OF STRAIGHT LINES

    OBJECTIVE RD SHARMA|Exercise Chapter Test|19 Videos

Similar Questions

Explore conceptually related problems

If 2a+3b+6c=0, then prove that at least one root of the equation ax^(2)+bx+c=0 lies in the interval (0,1) .

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

Consider the quadratic equation (c-3) x^2 - 2cx + (c - 2) = 0 , c ne 3 . Let S be the set of all integral values of c for which one root of the equation lies in the interval (0, 2) and its other root lies in the interval (2, 3). Then the number of elements in S is:

Consider the quadratic equation (c - 5)x^(2) - 2cx + (c - 4) = 0, c ne 5 . Let S be the set of all integral values of c for which one root of the equation lies in the interval (0, 2) and its other root lies in the interval (2, 3). Then the number of elements in S is

If exactly one root of the quadratic equation x ^(2) -(a+1 ) +2a =0 lies in the interval (0,3) then the set of value 'a' is given by :

If a+b+c=0, a,b,c in Q then roots of the equation (b+c-a) x ^(2) + (c+a-c) =0 are:

If a+b + c = 0, then show that the quadratic equation 3ax^(2) + 2bx +c=0 has at least one root in [0,1].

Find the condition if the equation 3x^(2)+4ax+b=0 has at least one root in (0,1).

OBJECTIVE RD SHARMA-MEAN VALUE THEOREMS-Exercise
  1. Let a and b be two distinct roots of a polynomial equation f(x) =0 The...

    Text Solution

    |

  2. If 2a+3b+6c=0, then prove that at least one root of the equation a x^2...

    Text Solution

    |

  3. Let f(x)a n dg(x) be two functions which are defined and differentiabl...

    Text Solution

    |

  4. Let f be differentiable for all x , If f(1)=-2a n df^(prime)(x)geq2 fo...

    Text Solution

    |

  5. If the function f(x)=x^3-6x^2+a x+b defined on [1,3] satisfies Rolles ...

    Text Solution

    |

  6. Let (a0)/(n+1)+(a1)/n+(a2)/(n-1)++(a(n-1))/2+an=0. Show that there e...

    Text Solution

    |

  7. The number of values of k for which the equation x^3-3x+k=0 has two di...

    Text Solution

    |

  8. Let f(x)=(x-4)(x-5)(x-6)(x-7) then. (A)fprime(x)=0 has four roots (B)T...

    Text Solution

    |

  9. Let fa n dg be differentiable on [0,1] such that f(0)=2,g(0),f(1)=6a n...

    Text Solution

    |

  10. If the polynomial equation an x^n + a(n-1) x^(n-1) + a(n-2) x^(n-2) + ...

    Text Solution

    |

  11. The equation x log x = 3-x has, in the interval (1,3) :

    Text Solution

    |

  12. If f(x) and g(x) ar edifferentiable function for 0lex le1 such that f(...

    Text Solution

    |

  13. If alpha beta( alpha lt beta) are two distinct roots of the equation. ...

    Text Solution

    |

  14. If (x) is a function given by f(x) = |{:(sinx , sin a, sin b),(cosx,c...

    Text Solution

    |

  15. The value of c in Largrange's theorem for the function f(x)= log(e) s...

    Text Solution

    |

  16. n is a positive integer. If the value of c presecribed in Rolle's th...

    Text Solution

    |

  17. The distance travelled by a particle upto tiem x is given by f(x)=x^(...

    Text Solution

    |

  18. The number of real root of the equation e^(x-1)+x-2=0, is

    Text Solution

    |

  19. If the polynomial equation an x^n + a(n-1) x^(n-1) + a(n-2) x^(n-2) + ...

    Text Solution

    |

  20. If 4a+2b+c=0 , then the equation 3ax^(2)+2bx+c=0 has at least one rea...

    Text Solution

    |