Home
Class 12
MATHS
If a x^2+b x+c=0a n db x^2+c x+a=0 have ...

If `a x^2+b x+c=0a n db x^2+c x+a=0` have a common root and a, b, and c are nonzero real numbers, then find the value of `(a^3+b^3+c^3)//a b c`

Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise 2.1|3 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise 2.2|5 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Comprehension|12 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|20 Videos

Similar Questions

Explore conceptually related problems

If ax^(2)+bx+c=0 and bx^(2)+cx+a=0 have a common root and a,b,and c are nonzero real numbers,then find the value of (a^(3)+b^(3)+c^(3))/abc

IF x^2 + a x + bc = 0 and x^2 + b x + c a = 0 have a common root , then a + b+ c=

If x^(2)+bx+c=0,x^(2)+cx+b=0(b!=c) have a common root then b+c=

If a+b+c=0 , then find the value of (x^(a))^(3)/(x^(-3b)x^(-3c))

If the equation ax^(2) + bx + c = 0 and 2x^(2) + 3x + 4 = 0 have a common root, then a : b : c

If x^(2)+3x+5=0 and ax^(2)+bx+c=0 have common root/roots and a,b,c in N then find the minimum value of a+b+c .

If the equation x^(2)+2x+3=0 and ax^(2)+bx+c=0 have a common root then a:b:c is

If alphaa n dbeta,alphaa n dgamma,alphaa n ddelta are the roots of the equations a x^2+2b x+c=0,2b x^2+c x+a=0a d nc x^2+a x+2b=0, respectively, where a, b, and c are positive real numbers, then alpha+alpha^2= a.a b c b. a+2b+c c. -1 d. 0

CENGAGE-THEORY OF EQUATIONS-Examples
  1. If alpha and beta are roots of the equatioin a cos theta + b sin theta...

    Text Solution

    |

  2. Determine the values o m for which equations 3x^2+4m x+2=0a n d2x^2+3x...

    Text Solution

    |

  3. If a x^2+b x+c=0a n db x^2+c x+a=0 have a common root and a, b, and c ...

    Text Solution

    |

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

    Text Solution

    |

  5. 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

    |

  6. The equations x^2 +3x+5=0 and ax^2+bx+c=0 have a common root. If a,b,c...

    Text Solution

    |

  7. If a ,b ,p ,q are nonzero real numbers, then how many oon roots would ...

    Text Solution

    |

  8. a ,b ,c are positive real numbers forming a G.P. ILf a x 62+2b x+c=0a ...

    Text Solution

    |

  9. Find the condition on a , b ,c ,d such that equations 2a x^2+b^2+c x+d...

    Text Solution

    |

  10. Number of positive integers x for which f(x)=x^3-8x^2+20 x-13 is a pri...

    Text Solution

    |

  11. If r is positive real number such that 4sqrt(r)-(1)/(4sqrt(r))= 4, the...

    Text Solution

    |

  12. If alpha, beta and gamma the roots of the equation x^(3) + 3x^(2) - 4x...

    Text Solution

    |

  13. If alpha,beta,gamma are the roots of the equation x^3 + 4x +1=0 then (...

    Text Solution

    |

  14. Equations x^3+5x 62+p x+q=0a n dx 63+7x^2+p x+r=0 have two roots in co...

    Text Solution

    |

  15. If alpha, beta and gamma are the roots of the equation x^(3) + 3x^(2) ...

    Text Solution

    |

  16. If euation x^(3) + ax^(2) + bx + c = 0, where a, b, c in Q (a ne 1)....

    Text Solution

    |

  17. Solve the equation x^3-13 x^2+15 x+189=0 if one root exceeds the other...

    Text Solution

    |

  18. In equation x^4-2x^3+4x^2+6x-21=0 if two its roots are equal in mag...

    Text Solution

    |

  19. If b^2<2a c , then prove that a x^2+b x^2+c x+d=0 has exactly one real...

    Text Solution

    |

  20. If f(x)=x^2+b x^2+c x+da n df(0),f(-1) are odd integers, prove that f(...

    Text Solution

    |