Home
Class 11
MATHS
If z^3+(3+2i)z+(-1+i a)=0 has one real r...

If `z^3+(3+2i)z+(-1+i a)=0` has one real roots, then the value of `a` lies in the interval `(a in R)` `(-2,1)` b. `(-1,0)` c. `(0,1)` d. `(-2,3)`

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

One of the root equation cosx-x+1/2=0 lies in the interval (0,pi/2) (b) (-pi/(2,0)) (c) (pi/2,pi) (d) (pi,(3pi)/2)

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

If one root of z^2 + (a + i)z+ b +ic =0 is real, where a, b, c in R , then c^2 + b-ac=

If the equation 2^(2x)+a*2^(x+1)+a+1=0 has roots of opposite sign, then the exhaustive set of real values of a is (a)(−∞,0) (b)(−1,−2/3) (c)(−∞,−2/3) (d)(−1,∞)

Let alpha,beta be real and z be a complex number. If z^2+alphaz""+beta=""0 has two distinct roots on the line Re z""=""1 , then it is necessary that : (1) b"" in (0,""1) (2) b"" in (-1,""0) (3) |b|""=""1 (4) b"" in (1,oo)

The number of real roots of the equation x^2tanx=1 lies between 0 and 2pi is/are (A) 1 (B) 2 (C) 3 (D) 4

One root of the equation ax^(2)-3x+1=0 is (2+i) . Find the value of 'a' when a is not real.

Prove that the equation Z^3+i Z-1=0 has no real roots.

If x^(2)+bx+1=0,binR has imaginary root z such that |z+1|=3 then |b| can be:

If x lies in the interval [0,\ 1] , then the least value of x^2+x+1 is (a) 3 (b) 3//4 (c) 1 (d) none of these

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If a ,b ,c in R^+a n d2b=a+c , then check the nature of roots of equa...

    Text Solution

    |

  2. If z is a complex number such taht z^2=( barz)^2, then find the loc...

    Text Solution

    |

  3. If z^3+(3+2i)z+(-1+i a)=0 has one real roots, then the value of a lies...

    Text Solution

    |

  4. Determine the value of k for which x+2 is a factor of (x+1)^7+(2x+k)^3...

    Text Solution

    |

  5. Find the complex number z satisfying R e(z^2 =0),|z|=sqrt(3.)

    Text Solution

    |

  6. Given that the expression 2x^3+3p x^2-4x+p hs a remainder of 5 when di...

    Text Solution

    |

  7. z1a n dz2 are two distinct points in an Argand plane. If a|z1|=b|z2|(w...

    Text Solution

    |

  8. Consider two complex numbers alphaa n dbeta as alpha=[(a+b i)//(a-b i...

    Text Solution

    |

  9. In how many points the graph of f(x)=x^3+2x^2+3x+4 meets the x-axis ...

    Text Solution

    |

  10. If x^2+x+1=0 then the value of (x+1/x)^2+(x^2+1/(x^2))^2+...+(x^27+1/(...

    Text Solution

    |

  11. If (a" "+" "i b)" "(c" "+" "i d)" "(e" "+" "if)" "(g" "+" "i h)" "=" "...

    Text Solution

    |

  12. Analyze the roots of the equation (x-1)^3+(x-2)^3+(x-4)^3+(x-5)^3=0 by...

    Text Solution

    |

  13. Solve the equation |z|=z+1+2idot

    Text Solution

    |

  14. If z=i^(i^(i)) where i=sqrt-1 then |z| is equal to

    Text Solution

    |

  15. Find the values of a for which the roots of the equation x^2+a^2=8x+6...

    Text Solution

    |

  16. If alpha and beta are different complex numbers with |beta|=1, then...

    Text Solution

    |

  17. If z=i log(2-sqrt3), then cosz= a. -1 b. (-1)/2 c. 1 d. 2

    Text Solution

    |

  18. If f(x)=x^3-x^2+a x+b is divisible by x^2-x , then find the value of...

    Text Solution

    |

  19. If z=x+i y and w=(1-i z)//(z-i) and |w| = 1 , then show that z is pure...

    Text Solution

    |

  20. If the equation z^4+a1z^3+a2z^2+a3z+a4=0 where a1,a2,a3,a4 are real co...

    Text Solution

    |