Home
Class 12
MATHS
If alpha" and "beta, alpha" and "gamma" ...

If `alpha" and "beta, alpha" and "gamma" and "alpha" and "delta` are the roots of the equations `ax^(2)+2bx+c=0, 2bx^(2)+cx+a=0" and "cx^(2)+ax+2b=0` respectively, where a,b and c are positive real numbers, then `alpha+alpha^(2)=`

A

`-1`

B

`0`

C

`1`

D

`abc`

Text Solution

Verified by Experts

The correct Answer is:
A
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 , alpha and gamma , alpha and delta are the roots of the equations ax^(2)+2bx+c=0 , 2bx^(2)+cx+a=0 and cx^(2)+ax+2b=0 respectively where a , b , c are positive real numbers, then alpha+alpha^(2) is equal to

If alpha and beta are thr roots of the equation ax^(2) + bx + c = 0 then ( alpha + beta )^(2) is ……… .

If alpha and beta are the roots of the equation ax^(2)+bx+c=0 then (alpha+beta)^(2) is …………..

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

If alpha and beta are the roots of the equation x^(2)-ax+b=0 ,find Q(b) (1)/(alpha)+(1)/(beta)

If alpha" and "beta are the solutions of the quadratic equation ax^(2)+bx+c=0 such that beta= alpha^(1/3) , then

If alpha" and "beta are the roots of the equation ax^(2)+bx+c=0, (c ne 0) , then the equation whose roots are (1)/(a alpha +b)" and "(1)/(a beta +b) is

If alpha and beta are the roots of the equation x^(2)-ax+b=0 ,find Q (a)(alpha)/(beta)+(beta)/(alpha)

Let alpha , beta (a lt b) be the roots of the equation ax^(2)+bx+c=0 . If lim_(xtom) (|ax^(2)+bx+c|)/(ax^(2)+bx+c)=1 then

NEW JOYTHI PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTIONS FROM COMPETITIVE EXAMS
  1. If 3p^(2)=5p+2" and "3q^(2)= 5q+2, where p ne q, then the equation wh...

    Text Solution

    |

  2. If x=8+3sqrt(7)" and "xy=1, then the value of (1)/(x^2)+(1)/(y^2) is

    Text Solution

    |

  3. If alpha" and "beta, alpha" and "gamma" and "alpha" and "delta are the...

    Text Solution

    |

  4. The solution set of the equation pqx^(2)-(p+q)^(2)x+(p+q)^(2)=0 is

    Text Solution

    |

  5. If roots alpha, beta of the equation (x^(2)-bx)/(ax-c)=(lambda-1)/(lam...

    Text Solution

    |

  6. Let a= e^(i(2pi)/(3)). Then the equation whose roots are a+a^(-2)" and...

    Text Solution

    |

  7. If alpha(1), alpha(2), alpha(3), alpha(4) are the roots of the equatio...

    Text Solution

    |

  8. The roots of the eqaution (q-r)x^(2)+(r-p)x+(p-q)=0 are

    Text Solution

    |

  9. Let omega be a imaginary root of x^(n)=1. Then (5- omega)(5- omega^2)"...

    Text Solution

    |

  10. If isqrt(-1), then 4+5(-(1)/(2)+(isqrt(3))/(2))^(334)+3(-(1)/(2)+(isqr...

    Text Solution

    |

  11. If z is a complex number such that Re(z)=Im(z), then

    Text Solution

    |

  12. If alpha" and "beta are the roots of the equation x^(2)-7x+1=0, then t...

    Text Solution

    |

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

    Text Solution

    |

  14. If omega is a complex cube root of unity, then the value of sin{(omega...

    Text Solution

    |

  15. Let z=(11-3i)/(1+i). If alpha is a real number such z-ialpha is real, ...

    Text Solution

    |

  16. Let z(1)" and "z(2) be the roots of the equation z^(2)+pz+q=0, where p...

    Text Solution

    |

  17. If alpha, beta, gamma are the cube roots of a negative number p, then ...

    Text Solution

    |

  18. The magnitude and amplitude of ((1+isqrt(3))(2+2i))/((sqrt(3)-i)) are ...

    Text Solution

    |

  19. If 1+x^(2)=sqrt(3)x, then sum(n=1)^(24)(x^(n)-(1)/(x^n))^(2) is equal ...

    Text Solution

    |

  20. If alpha and beta are the roots of the equation ax^(2)+bx+c=0 then (a...

    Text Solution

    |