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.

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 equations 2x^(2)-7x+1=0 and ax^(2)+bx+2=0 have a common root, then

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

Find the condition so that the two equations a_1 x^2+b_1 x+c_1=0 and a_2 x^2+b_2 x+c_2=0 will have a common root.

Find the condition if equations ax^2+bx+c =0 and x^2+2x+3 =0 have a common root. (a,b,cinR)

Find the condition such that the quadratic equations ax^2+bx+c =0 and x^2/a+x/b+1/c =0 have exactly one root in common.

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

If the quadratic equations ax^2+2cx+b =0 and ax^2+2bx+c =0 (b ne 0) have a common root, then a+4b+4c is equal to

If a,b,c are in G.P., then the equations ax^2+2bx+c =0 and dx^2+2ex+f =0 have a common root if d/a,e/b,f/c are in

If ax^2+bx+c =0 and cx^2+bx+a =0 (a,b,cinR) have a common non-real roots,then

CENGAGE PUBLICATION-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 ,and b is nonzero real and i^2=-1. If the imaginary part ...

    Text Solution

    |

  5. Prove that ifz1,z2 are two complex numbers and cgt0 then abs((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+7i and |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 real...

    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

    |