Home
Class 12
MATHS
If a is a root of the equation x^(2)-3x+...

If a is a root of the equation `x^(2)-3x+1=0`, then the value of `(a^3)/(a^6+1)` is equal to

A

`(1)/(14)`

B

`(1)/(15)`

C

`(1)/(16)`

D

`(1)/(18)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NEW JOYTHI PUBLICATION|Exercise EXERCISE|50 Videos
  • BINOMIAL THEOREM

    NEW JOYTHI PUBLICATION|Exercise QUESTIONS FROM COMPETITIVE EXAMS|51 Videos
  • CONIC SECTIONS

    NEW JOYTHI PUBLICATION|Exercise EXERCISE - HYPERBOLA|9 Videos

Similar Questions

Explore conceptually related problems

If alpha" and "beta are the roots of the equation x^(2)+3x-4=0 , then (1)/(alpha)+(1)/(beta) is equal to

If alpha" and "beta are the roots of the equation x^(2)+2x+4=0, " then "(1)/(alpha^3)+(1)/(beta^3) is equal to

If alpha and beta be the roots of equation x^(2) + 3x + 1 = 0 then the value of ((alpha)/(1 + beta))^(2) + ((beta)/(1 + alpha))^(2) is equal to

If alpha" and "beta are the roots of the quadratic equation 4x^(2)+3x+7=0 , then the value of (1)/(alpha)+(1)/(beta)=

Find the roots of the equation x+(1)/(x)=3, x ne 0

If alpha is a root of the equation 4x^2+2x-1=0, then prove that 4alpha^3-3alpha is the other root.

If -4 is a root of the equation x^(2)+px-4=0 and if the equation x^(2)+px+q=0 are equal roots, find the values of p and q.

If alpha, beta and gamma are the roots of the equation x^(3) + 3x^(2) - 24x + 1 = 0 thebn find the value of (3sqrt(alpha)+3sqrt(beta)+ 3sqrt(gamma)).

If x_(1) , x_(2) and x_(3) are the positive roots of the equation x^(3)-6x^(2)+3px-2p=0 , pinR , then the value of sin^(-1)((1)/(x_(1))+(1)/(x_(2)))+cos^(-1)((1)/(x_(2))+(1)/(x_(3)))-tan^(-1)((1)/(x_(3))+(1)/(x_(1))) is equal to

The equation 2x^(2)+3x+1=0 has an irrational root.

NEW JOYTHI PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTIONS FROM COMPETITIVE EXAMS
  1. Let alpha" and "beta be the roots of the equation px^(2)+qx+r=0. If p,...

    Text Solution

    |

  2. If the roots of the equation x^(2)+px+c=0 are 2,-2 and the roots of th...

    Text Solution

    |

  3. If a is a root of the equation x^(2)-3x+1=0, then the value of (a^3)/(...

    Text Solution

    |

  4. If the sum of the roots of the equation (a+1)x^(2)+(2a+3)x+(3a+4)=0, i...

    Text Solution

    |

  5. The product of the roots of the equation x|x|-5x-6=0 is equal to

    Text Solution

    |

  6. If z=((sqrt(3)+i)^(3)(3i+ 4)^(2))/((8+6i)^(2)), then |z| is equal to

    Text Solution

    |

  7. Let w ne pm 1 be a complex number. If |w|=1" and "z=(w-1)/(w+1), then ...

    Text Solution

    |

  8. If z= e^((2pi i)/(3)), then 1+z+3z^(2)+2z^(3)+2z^(4)+3z^(5) is equal t...

    Text Solution

    |

  9. If z(1)= 2sqrt(2)(1+i)" and "z(2)=1+isqrt(3), then z(1)^(2)z(2)^(3) is...

    Text Solution

    |

  10. If the complex numbers z(1), z(2)" and "z(3) denote the vertices of an...

    Text Solution

    |

  11. If the roots of x^(2)-ax+b=0 are two consecutive odd integers, then a^...

    Text Solution

    |

  12. If alpha" and "beta are the roots of x^(2)-ax+b^(2)=0, then alpha^(2)+...

    Text Solution

    |

  13. If alpha" and "beta are the roots of the equation x^(2)+3x-4=0, then ...

    Text Solution

    |

  14. The value of x such that 3^(2x)-2(3^(x+2))+81=0 is

    Text Solution

    |

  15. If the roots of the equation x^(2)+2bx+c=0 are alpha" and "beta, " the...

    Text Solution

    |

  16. The equation whose roots are the squares of the roots of the eqation 2...

    Text Solution

    |

  17. z and omega are two nonzero complex number such that |z|=|omega|" and ...

    Text Solution

    |

  18. If |z-4| lt |z-2|, its solution is given by

    Text Solution

    |

  19. The locus of the centre of a circle which touches the circle |z-z(1)|=...

    Text Solution

    |

  20. If alpha ne beta" but "alpha^(2)=5 alpha-3" and "beta^(2)= 5 beta-3 th...

    Text Solution

    |