Home
Class 11
MATHS
If the roots of the equation x^3+P x^2+Q...

If the roots of the equation `x^3+P x^2+Q x-19=0` are each one more that the roots of the equation `x^3-A x^2+B x-C=0,w h e r eA ,B ,C ,P ,a n dQ` are constants, then find the value of `A+B+Cdot`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise All Questions|365 Videos

  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

Similar Questions

Explore conceptually related problems

If p + iq be one of the roots of the equation x^(3) +ax +b=0 ,then 2p is one of the roots of the equation

The roots of the equation (b-c) x^2 +(c-a)x+(a-b)=0 are

If the ratio of the roots of the equation x^2+p x+q=0 are equal to ratio of the roots of the equation x^2+b x+c=0 , then prove that p^2c=b^2qdot

If the ratio of the roots of the equation x^2+p x+q=0 are equal to ratio of the roots of the equation x^2+b x+c=0 , then prove that p^(2)c=b^2qdot

If the roots of the equation x^2+2c x+a b=0 are real unequal, prove that the equation x^2-2(a+b)x+a^2+b^2+2c^2=0 has no real roots.

If c ,d are the roots of the equation (x-a)(x-b)-k=0 , prove that a, b are roots of the equation (x-c)(x-d)+k=0.

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

If the roots of the cubic equation x^(3) -9x^(2) +a=0 are in A.P., Then find one of roots and a

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

Find the cubic equation whose roots are the squares of the roots of the equation x^3 +p_1 x^2 +p_2 x+p_3 =0

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Equations x^3+5x^2+p x+q=0a n dx^3+7x^2+p x+r=0 have two roots in com...

    Text Solution

    |

  2. If alpha,beta,gamma are the roots of he euation x^3+4x+1=0, then find ...

    Text Solution

    |

  3. If the roots of the equation x^3+P x^2+Q x-19=0 are each one more that...

    Text Solution

    |

  4. If a ,b ,p ,q are non zero real numbers, then how many comman roots wo...

    Text Solution

    |

  5. If x^2+p x+q=0a n dx^2+q x+p=0,(p!=q) have a common roots, show that ...

    Text Solution

    |

  6. a,b,c are positive real numbers forming a G.P. ILf ax^2+2bx+c=0...

    Text Solution

    |

  7. If equations x^2+a x+12=0. x^2+b x+15=0a n dx^2+(a+b)x+36=0, have a co...

    Text Solution

    |

  8. If x is real and the roots of the equation a x^2+b x+c=0 are imaginary...

    Text Solution

    |

  9. Solve (x^2+2)^2+8x^2=6x(x^2+2)

    Text Solution

    |

  10. Find the value of 2+1/(2+1/(2+1/(2+oo)))

    Text Solution

    |

  11. If both the roots of a x^2+a x+1=0 are less than 1, then find the exha...

    Text Solution

    |

  12. If both the roots of x^2+a x+2=0 lies in the interval (0, 3), then fin...

    Text Solution

    |

  13. Solve (x^2+3x+2)/(x^2-6x-7)=0.

    Text Solution

    |

  14. Solve sqrt(x-2)+sqrt(4-x)=2.

    Text Solution

    |

  15. Solve sqrt(x-2)(x^2-4x-5)=0.

    Text Solution

    |

  16. Solve the equation x(x+2)(x^2-1)=-1.

    Text Solution

    |

  17. The number of distinct real roots of x^4 - 4 x^3 + 12 x^2 + x - 1 = 0...

    Text Solution

    |

  18. Prove that graphs of y=x^2+2a n dy=3x-4 never intersect.

    Text Solution

    |

  19. In how many points the line y+14=0 cuts the curve whose equation is x(...

    Text Solution

    |

  20. Consider the graph of y = f(x) as shown in the following figure. ...

    Text Solution

    |