Home
Class 12
MATHS
If a+b+c=0, then, the equation 3ax^(2)+...

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

A

(-1,1)

B

(0,2)

C

`(1/2,3/2)`

D

(0,1).

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • Ellipse and Hyberbola

    A DAS GUPTA|Exercise EXERCISE|65 Videos

  • Function

    A DAS GUPTA|Exercise Exercise|57 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 roots of the equation 3ax^(2)+4bx+5c=0 are

If 4a+2b+c=0 , then the equation 3ax^(2)+2bx+c=0 has at least one real lying in the interval

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

If c>0 and the equation 3ax^(2)+4bx+c=0 has no real root,then

If a,b,c in R and a+b+c=0, then the quadratic equation 3ax^(2)+2bx+c=0 has (a) at least one root in [0,1] (b) at least one root in [1,2](c) at least one root in [(3)/(2),2] (d) none of these

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

If c gt0 and 4a+clt2b then ax^(2)-bx+c=0 has a root in the interval

A DAS GUPTA-Equations, Inequation and Expressions-Exercise
  1. The real value of a for which x^2+i(a-1)x+5=0 will have a pair of con...

    Text Solution

    |

  2. If a, b, c are positive then both roots of the equation ax^2 + bx+c=0

    Text Solution

    |

  3. The expression a^2x^2+bx+1 will be positive for all x in R if

    Text Solution

    |

  4. If x ,y ,a n dz are real and different and u=x^2+4y^2+9z^2-6y z-3z x-2...

    Text Solution

    |

  5. The least value of ax^2+bx+c,(a>0) is

    Text Solution

    |

  6. If x be real, then the maximum value of 5+4x-4x^2 will be equal to

    Text Solution

    |

  7. If x^2+p x=1 is a factor of the expression a x^3+b x=c , then a^2-c^2=...

    Text Solution

    |

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

    Text Solution

    |

  9. If the value of ax^2+bx+c is always an integer for integral values of ...

    Text Solution

    |

  10. If a gt 1 , then the roots of the equation (1-a)x^(2)+3ax-1=0 are

    Text Solution

    |

  11. Fill in the blank : If f(x) = x+1/x , x in R Then the set of possible ...

    Text Solution

    |

  12. Fill in the blank : If 1+ i is a root of the equation ix^2-3x+p = 0 wh...

    Text Solution

    |

  13. Equation cos 2x+7=a(2-sin x) can have a real solution for

    Text Solution

    |

  14. If alpha,beta be the roots of x^2 - x-1 = 0 and An = alpha^n +beta^n, ...

    Text Solution

    |

  15. For all lambda in R, The equation ax^2+ (b - lambda)x + (a-b-lambda)= ...

    Text Solution

    |

  16. Prove that (a^2 + b^2) x^2 - 2b(a+c)x + (b^2+ c^2) ge 0 for all x in R...

    Text Solution

    |

  17. Let f(x)= x^4- 3x^3 + 2x^2-3x+ a.If f(sqrt-1)= 0 and a in R then prove...

    Text Solution

    |

  18. If a1x^3 + b1x² + c1x + d1 = 0 and a2x^3 + b2x^2+ c2x + d2 = 0 have a ...

    Text Solution

    |

  19. Find all numbers p for each of which the least value of the quadratic ...

    Text Solution

    |

  20. Prove that the equation x^3 + 2x^2 +x + 4 = 0 has exactly one root in ...

    Text Solution

    |