Home
Class 11
MATHS
Find the condition on a , b ,c ,d such t...

Find the condition on `a , b ,c ,d` such that equations `2a x^3+bx^2+c x+d=0` and `2ax^2+3b x+4c=0` have a common root.

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

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

If a,b,c, in R and equations ax^(2) + bx + c =0 and x^(2) + 2x + 9 = 0 have a common root then

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

If a,b,c in R and the equation ax^2+bx+c = 0 and x^2+ x+ 1=0 have a common root, then

If the equation ax^2+2bx+c=0 and ax^2+2cx+b=0 b!=c have a common root ,then a/(b+c =

Find a relation between a,b,c so that two quadratic equations ax^(2) + bx + c =0 and 1003x^(2) + 1505x + 2007 =0 have a common root.

If a, b, c are positive real numbers such that the equations ax^(2) + bx + c = 0 and bx^(2) + cx + a = 0 , have a common root, then

If a ,b ,c in R and equations a x^2+b x+c=0 and x^2+2x+3=0 have a common root, then find a : b : c

If a,b,c in R and equations ax^2 + bx + c = 0 and x^2 + 2x + 9 = 0 have a common root, show that a:b:c=1 : 2 : 9.

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Find the amplitude of sinalpha+i(1-cosalpha)

    Text Solution

    |

  2. Modulus of non zero complex number z satisfying barz +z=0 and |z|^2-4...

    Text Solution

    |

  3. Find the condition on a , b ,c ,d such that equations 2a x^3+bx^2+c x+...

    Text Solution

    |

  4. Let z=9+b i ,w h e r eb is nonzero real and i^2=-1. If the imaginary p...

    Text Solution

    |

  5. If z1a n dz2 are two complex numbers and c >0 , then prove that |z1+z2...

    Text Solution

    |

  6. Let f(x), g(x), and h(x) be the quadratic polynomials having positive ...

    Text Solution

    |

  7. Find the minimum value of |z-1 if ||z-3|-|z+1||=2.

    Text Solution

    |

  8. If x=omega-omega^2-2 then , the value of x^4+3x^3+2x^2-11x-6 is (where...

    Text Solution

    |

  9. If a ,b ,c be the sides of A B C and equations a x^2+b x+c=0 and 5x^2...

    Text Solution

    |

  10. Find the greatest and the least value of |z1+z2| ifz1=24+7ia n d|z2|=6...

    Text Solution

    |

  11. If the complex numbers x and y satisfy x^3-y^3=98 ia n dx-y=7i ,t h e ...

    Text Solution

    |

  12. If b^2<2a c , then prove that a x^3+b x^2+c x+d=0 has exactly one re...

    Text Solution

    |

  13. If z is any complex number such that |z+4|lt=3, then find the greatest...

    Text Solution

    |

  14. If z1, z2 and z3, are the vertices of an equilateral triangle ABC suc...

    Text Solution

    |

  15. If two roots of x^3-a x^2+b x-c=0 are equal in magnitude but opposite ...

    Text Solution

    |

  16. For any complex number z find the minimum value of |z|+|z-2i|

    Text Solution

    |

  17. The greatest positive argument of complex number satisfying |z-4|=R e(...

    Text Solution

    |

  18. If alpha,betaa n dgamma are the roots of x^3+8=0 then find the equat...

    Text Solution

    |

  19. Prove that the distance of the roots of the equation |sintheta1|z^3+|s...

    Text Solution

    |

  20. Let z1a n dz2 be two distinct complex numbers and let z=(1-t)z1+t z2 f...

    Text Solution

    |