Home
Class 11
MATHS
If x^2+a x+bc=0 a n d x^2+b x+c a=0(a!=b...

If `x^2+a x+bc=0 a n d x^2+b x+c a=0(a!=b)` have a common root, then prove that their other roots satisfy the equation `x^2+c x+a b=0.`

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 x^2+a x+b=0a n dx^2+b x+c a=0(a!=b) have a common root, then prove that their other roots satisfy the equation x^2+c x+a b=0.

If the equation x^(2)+ax+b=0 and x^(2)+bx+a=0 have a common root, then their other roots satisfy the equation

If x^(2)+ax+b=0 and x^(2)+bx+a=0,(a ne b) have a common root, then a+b is equal to

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

If the equation x^2+ax+bc=0" and " x^2-bx+ca=0 have a common root, then a+b+c =

If a_1x^2 + b_1 x + c_1 = 0 and a_2x^2 + b_2 x + c_2 = 0 has a common root, then the common root is

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

If a lt c lt b then the roots of the equation (a−b)x^2 +2(a+b−2c)x+1=0 are

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

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

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If x is real and (x^2+2x+c)//(x^2+4x+3c) can take all real values, of ...

    Text Solution

    |

  2. If alpha,beta are the roots of the equation 2x^2+2(a+b)x+a^2+b^2=0 , t...

    Text Solution

    |

  3. If x^2+a x+bc=0 a n d x^2+b x+c a=0(a!=b) have a common root, then pro...

    Text Solution

    |

  4. Let alpha,beta are the roots of x^2+b x+1=0. Then find the equation wh...

    Text Solution

    |

  5. Find the greatest value of a non-negative real number lambda for which...

    Text Solution

    |

  6. If a ,b ,c in R such that a+b+c=0a n da!=c , then prove that the root...

    Text Solution

    |

  7. If the fraction (x^3+(a-10)x^2-x+a-6)/(x^3+(a-6)x^2-x+a-10) reduces to...

    Text Solution

    |

  8. If the equation (a-5)x^2+2(a-10)x+a+10=0 has roots of opposite sign, t...

    Text Solution

    |

  9. If alphaa n dbeta are the roots of ax^2+bx+c=0a n dSn=alpha^n+beta^n,...

    Text Solution

    |

  10. If alpha is a root of the equation 4x^2+2x-1=0, then prove that 4alp...

    Text Solution

    |

  11. If both the roots of x^2-a x+a=0 are greater than 2, then find the val...

    Text Solution

    |

  12. If (y^2-5y+3)(x ^2+x+1)<2x for all x in R , then fin the interval i...

    Text Solution

    |

  13. The values of 'a' for which 4^x-(a-4) 2^x+(9a)/4<0 AAx in(1,2) is

    Text Solution

    |

  14. Find the number of positive integral values of k for which kx ^(2) +(k...

    Text Solution

    |

  15. If x^2+2ax+a lt 0 AA x in [1, 2] then find set of all possible values ...

    Text Solution

    |

  16. Given that a ,b ,c are distinct real numbers such that expressions a ...

    Text Solution

    |

  17. Find the number of quadratic equations, which are unchanged by squarin...

    Text Solution

    |

  18. Solve the following: (sqrt(x^2-5x+6)+sqrt(x^2-5x+4))^(x/2)+(sqrt(x^2-...

    Text Solution

    |

  19. Show that the equation A^2//(x-a)+B^2//(x-b)+C^2//(x-c)+...+H^2//(x-h)...

    Text Solution

    |

  20. Find the values of a if x^2-2(a-1)x+(2a+1)=0 has positive roots.

    Text Solution

    |