Home
Class 12
MATHS
Let a,b,c be the sides of a triangle n...

Let a,b,c be the sides of a triangle no two of them are equal and `lambda in R` if the roots of the equation `x^(2)+2(a+b+c)+3lambda`(ab+bc+ca=0) are real then

A

`lambda lt (4)/(3)`

B

`lambda gt (5)/(3)`

C

`lambda in((1)/(3), (5)/(3))`

D

`lambda in`((4)/(3), (5)/(3))`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • PROGRESSIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|97 Videos

  • SETS,RELATIONS AND FUNCTIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|285 Videos

Similar Questions

Explore conceptually related problems

Let a, b,c be sides of a triangle. No two of them are equal and lambda in R. If the roots of the equation x^(2) + 2 (a + b + c) x + 3 lambda (ab + bc + ca ) = 0 are real , then :

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

If a, b, c are real and a!=b , then the roots of the equation, 2(a-b)x^2-11(a + b + c) x-3(a-b) = 0 are :

If a,b,c are positive real numbers, then the roots of the equation ax^(2) + bx + c =0

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

If the roots of the equations (b-c) x^(2) + (c-a) x+( a-b) =0 are equal , then prove that 2b=a+c

If one of the roots of the equation a(b-c)x^(2)+b(c-a)x+c(a-b)=0 is 1, the other root is

if one of the root of the equation a(b-c)x^(2)+b(c-a)x+c(a-b)=0 is 1,the other root is

If the ratio of the roots of the equation a x^(2)+b x+c=0 is equal to the ratio of the roots of the equation x^(2)+x+1=0 , then a, b , c are in

HIMALAYA PUBLICATION-QUADRATIC EQUATIONS AND EXPRESSION-Question Bank
  1. If x^(2)+2 a x+(10-3 a) gt 0 for all x, then

    Text Solution

    |

  2. Let f(x)=a x^(2)+b x+c, a ne 0 and Delta=b^(2)-4 a c . If alpha+beta, ...

    Text Solution

    |

  3. Let a,b,c be the sides of a triangle no two of them are equal and la...

    Text Solution

    |

  4. If alpha, beta are the roots of the equation x^(2)+x+1=0, then the equ...

    Text Solution

    |

  5. Let alpha,beta be the roots of the equation x^(2)-px+r=0 and (alpha)/...

    Text Solution

    |

  6. The smallest value of k for which both the roots of the equation x^(2)...

    Text Solution

    |

  7. The minimum positive value of (x^(2)+2 x+4)/(x+2) is

    Text Solution

    |

  8. Let p and q be real number such that p ne 0 , p^(3) ne q and p^(3...

    Text Solution

    |

  9. If p and q are the roots of the equation x^(2)+p x+q=0 then

    Text Solution

    |

  10. If the difference between the roots of x^(2)+a x+b=0 is same as that o...

    Text Solution

    |

  11. If alpha ne beta and alpha^(2) = 5 alpha - 3, beta^(2) = 5 beta - 3 , ...

    Text Solution

    |

  12. The number of real roots of the equation |x|^(2)-3|x|+2=0 is

    Text Solution

    |

  13. If one root of the equation x^(2)+p x+12=0 is 4, while the equation x^...

    Text Solution

    |

  14. If 2 a+3 b+6 c=0, a, b, c in R then the equation a x^(2)+b x+c=0 has a...

    Text Solution

    |

  15. If (1-p) is a root of the quadratic equation x^(2)+p x+(1-p)=0 then it...

    Text Solution

    |

  16. The value of a for which the sum of the squares of the roots of the eq...

    Text Solution

    |

  17. If both the roots of the quadratic equation x^(2)-2 k x+(k^(2)+k-5)=0 ...

    Text Solution

    |

  18. If x is real, the maximum value of (3 x^(2)+9 x+17)/(3 x^(2)+9 x+7) is

    Text Solution

    |

  19. All the values of m for which both roots of the equation x^(2)-2 m x+(...

    Text Solution

    |

  20. If the roots of the quadratic equation x^(2)+p x+q=0 are tan 30^(circ)...

    Text Solution

    |