Home
Class 11
MATHS
Suppose A, B, C are defined as A=a^2b+a ...

Suppose A, B, C are defined as `A=a^2b+a b^2-a^2c-a c^2 , B=b^2c+b c^2-a^2b-a b^2 - bc^2, and C=a^2c +'a c^2-b^2' c-b c^2, w h e r ea > b > c >0` and the equation `A x^2+B x+C=0` has equal roots, then `a ,b ,c` are in `AdotPdot` b. `GdotPdot` c. `HdotPdot` d. `AdotGdotPdot`

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise All Questions|363 Videos
  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

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

If a+b+c=0 then check the nature of roots of the equation 4a x^2+3b x+2c=0 where a ,b ,c in Rdot

Suppose a,b,c are in A.P and a^2 , b^2 , c^2 are in G.P if a

Show that the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal if a,b,c are in H.P.

If a, b, c and d are in G.P. show that (a^2+b^2+c^2)(b^2+c^2+d^2)=(a b+b c+c d)^2 .

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

If A,B,C, are the angles of a triangle such that cot(A/2)=3tan(C/2), then sinA ,sinB ,sinC are in (a) AdotPdot (b) GdotPdot (c) HdotPdot (d) none of these

If the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal, show that 2//b=1//a+1// c dot

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

If |[b^2+c^2,a b,a c],[ a b, c^2+a^2,b c],[c a, c b, a^2+b^2]|=k a^2b^2c^2, then the value of k is a b c b. a^2b^2c^2 c. b c+c a+a b d. none of these

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If a(p+q)^2+2b p q+c=0 and a(p+r)^2+2b p r+c=0 (a!=0) , then which one...

    Text Solution

    |

  2. If alpha1,alpha2 are the roots of equation x ^2-p x+1=0a n dbeta1,bet...

    Text Solution

    |

  3. Suppose A, B, C are defined as A=a^2b+a b^2-a^2c-a c^2 , B=b^2c+b c^2-...

    Text Solution

    |

  4. The integral value of m for which the root of the equation m x^2+(2m-1...

    Text Solution

    |

  5. If b1. b2=2(c1+c2) then at least one of the equation x^2+b1x+c1=0 and ...

    Text Solution

    |

  6. If the root of the equation (a-1)(x^2-x+1)^2=(a+1)(x^4+x^2+1) are real...

    Text Solution

    |

  7. If alpha and beta are roots of the equation a x^2+b x+c=0, then the ro...

    Text Solution

    |

  8. If a ,b ,c ,d in R , then the equation (x^2+a x-3b)(x^2-c x+b)(x^2-dx...

    Text Solution

    |

  9. Graph of y = f(x) is as shown in the following figure. Find th...

    Text Solution

    |

  10. In how many points graph of y=x^3-3x^2+5x-3 intersect the x-axis?

    Text Solution

    |

  11. The quadratic polynomial p(x) has the following properties:p(x)geq0 fo...

    Text Solution

    |

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

    Text Solution

    |

  13. A polynomial in x of degree 3 vanishes when x=1 and x=-2 , ad has the ...

    Text Solution

    |

  14. Let f(x)=a^2+b x+c where a ,b , c in R and a!=0. It is known that f(5...

    Text Solution

    |

  15. If x=1 and x=2 are solutions of equations x^3+a x^2+b x+c=0 and a+b=1,...

    Text Solution

    |

  16. If x in R ,a n da ,b ,c are in ascending or descending order of magni...

    Text Solution

    |

  17. Prove that graphs y=2x-3 and y=x^2-x never intersect.

    Text Solution

    |

  18. Which of the following pair of graphs intersect ? (i) y = x^(2) - x ...

    Text Solution

    |

  19. If alpha and beta are the rootsof he equations x^2-a x+b=0a n dAn=alph...

    Text Solution

    |

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

    Text Solution

    |