Home
Class 11
MATHS
zo is one of the roots of the equation z...

zo is one of the roots of the equation `z^n cos theta_0+ z^(n-1) cos theta_1 +. . . . . . + z cos theta_(n-1) + cos theta_(n) = 2`, where `theta in R` , then
(A) `|z_0| lt 1/2`
(B) `|z_0| gt 1/2`
(C) `|z_0| = 1/2`
(D)None of these

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

Prove that, (2 cos theta - 1)(2 cos 2 theta-1)(2 cos2^(2) theta-1)...(2 cos 2^(n-1) theta-1) = (2 cos 2^(n) theta + 1)/(2 cos theta + 1)

The number of solution the equation cos(theta).cos(pitheta)=1 has 0 (b) 2 (c) 4 (d) 2

If z_1 is a root of the equation a_0z^n+a_1z^(n-1)+........+ (a_(n-1)) z + a_n=3, where |a_i| lt 2 for i=0,1,.....n, then (a). |z|=3/2 (b). |z| lt 1/4 (c). |z| gt 1/4 (d). |z| > 1/3

If cos theta = n cos ( theta + 2 phi) "show that"(n+1) tan ( theta + phi)= (n-1) cot phi

Solve : cos theta cos 2 theta cos 3 theta =(1)/(4) (0 le theta le pi)

If cos theta ne 1/2, then the solution of the equation cos 2 theta =(sqrt2 +1) (cos theta -(1)/(sqrt2)) are-

Solve : 5cos2theta+2cos^2(theta/2)+1=0,-pi lt theta lt pi

If theta = pi/(2^(n) + 1), "show that",2^(n) cos theta cos 2 theta cos2^(2) theta cos2^(3) theta.... cos2^(n-1) theta = 1.

If (cos theta + i sin theta)(cos 2 theta +i sin 2 theta ) …(cos n theta + i sin n theta)=1 then the value of theta is (m are integers)-

IF 2 cos 4 theta + 9 cos 2 theta -7=0 , then show that , theta =(1)/(2) cos ^(-1)""(3)/(4)

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If p ,q ,r ,s are rational numbers and the roots of f(x)=0 are eccentr...

    Text Solution

    |

  2. If |z-(1/z)|=1, then a. (|z|)(m a x)=(1+sqrt(5))/2 b. (|z|)(m in)=(s...

    Text Solution

    |

  3. zo is one of the roots of the equation z^n cos theta0+ z^(n-1) cos th...

    Text Solution

    |

  4. If a0, a1, a2, a3 are all the positive, then 4a0x^3+3a1x^2+2a2x+a3=0 ...

    Text Solution

    |

  5. If 1,z1,z2,z3,.......,z(n-1) be the n, nth roots of unity and omega b...

    Text Solution

    |

  6. If a x ^2+b x+c=0 has imaginary roots and a-b+c >0 then the set of poi...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  12. If amp(z1z2)=0 and absz1=absz2=1, then

    Text Solution

    |

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

    Text Solution

    |

  14. Prove that ln(1+x) < x for x > 0.

    Text Solution

    |

  15. Form a quadratic equation whose roots are -4 and 6.

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |