Home
Class 11
MATHS
If the equation z^3 + (3 + i)(z^2) - 3z ...

If the equation `z^3 + (3 + i)(z^2) - 3z - (m + i)= 0,` `m in R` , has at least one real root, then sum of possible values of m, is

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 z^(3)+(3+i)z^(2)-3z-(m+i)=0, " where " i=sqrt(-1) " and " m in R , has atleast one real root, value of m is

The equation z^2 - (3 + i) z + (m + 2i) = 0 m in R , has exactly one real and one non real complex root, then product of real root and imaginary part of non-real complex root is:

If 3x^(2) -17x+10 =0 and x^(2)-5x+m =0 has a common root, then sum of all possible real values of 'm' is:

Let z be a complex number satisfying the equation z^2-(3+i)z+m+2i=0\ ,where m in Rdot . Suppose the equation has a real root. Then the value of m is-

Let z be a complex number satisfying the equation z^(2)-(3+i)z+lambda+2i=0, whre lambdain R and suppose the equation has a real root , then find the non -real root.

Let z be a complex number satisfying the equation z^2-(3+i)z+m+2i=0,w h e r em in Rdot Suppose the equation has a real root. Then find non-real root.

If |z-4 +3i| le 2 then the least and the greatest values of |z| are q

If one root of the equation z^2-a z+a-1= 0 is (1+i), where a is a complex number then find the root.

For a complex number z, the equation z^(2)+(p+iq)z+ r+" is "=0 has a real root (where p, q, r, s are non - zero real numbers and i^(2)-1 ), then

If |z - 3+ 2i| leq 4 , (where i = sqrt-1 ) then the difference of greatest and least values of |z| is

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If a x ^2+b x+c=0 has imaginary roots and a-b+c >0 then the set of p...

    Text Solution

    |

  2. All the values of ' a ' for which the quadratic expression a x^2+(a-2)...

    Text Solution

    |

  3. If the equation z^3 + (3 + i)(z^2) - 3z - (m + i)= 0, m in R , has at ...

    Text Solution

    |

  4. If a+b+c=0,a^2+b^2+c^2=4,t h e na^4+b^4+c^4 is.

    Text Solution

    |

  5. Let P(x) and Q(x) be two polynomials. If f(x) = P(x^4) + xQ(x^4) is di...

    Text Solution

    |

  6. Find the solution set of the system x+2y+z=1 2x-3y-w=2 xgeq0,ygeq0,zge...

    Text Solution

    |

  7. If a m p(z1z2)=0a n d|z1|=|z2|=1,t h e n z1+z2=0 b. z1z2=1 c. z1=z 2...

    Text Solution

    |

  8. mn squares of equal size are arranged to form a rectangle of dimension...

    Text Solution

    |

  9. If the points A(z),B(-z),a n dC(1-z) are the vertices of an equilater...

    Text Solution

    |

  10. Form a quadratic equation whose roots are -4a n d6.

    Text Solution

    |

  11. If |(z-z1)/(z-z2)|=3,w h e r ez1a n dz2 are fixed complex numbers and ...

    Text Solution

    |

  12. If a,b,c are odd integere then about that ax^2+bx+c=0, does not have r...

    Text Solution

    |

  13. if arg(z+a)=pi/6 and arg(z-a)=(2pi)/3 then

    Text Solution

    |

  14. Values (s)(-i)^(1/3) is/are (sqrt(3)-i)/2 b. (sqrt(3)+i)/2 c. (-sqrt(...

    Text Solution

    |

  15. if costheta , sinphi , sintheta are in g.p then check the nature of ro...

    Text Solution

    |

  16. Given z=(1+isqrt(3))^(100), then [Re(z)//Im(z)] equals (a)2^(100) b. 2...

    Text Solution

    |

  17. If a ,b ,c are non zero rational no then prove roots of equation (a b ...

    Text Solution

    |

  18. If a b+b c+c a=0, then solve a(b-2c)x^2+b(c-2a)x+c(a-2b)=0.

    Text Solution

    |

  19. If (costheta +isintheta)(cos2theta +isin2theta).....(cosntheta + isinn...

    Text Solution

    |

  20. The polynomial x^6+4x^5+3x^4+2x^3+x+1 is divisible by where omega is o...

    Text Solution

    |