Home
Class 11
MATHS
If alpha,a n dbeta be the roots of the e...

If `alpha,a n dbeta` be the roots of the equation `x^2+p x-1//2p^2=0,w h e r ep in Rdot` Then the minimum value of `alpha^4+beta^4` is `2sqrt(2)` b. `2-sqrt(2)` c. `2` d. `2+sqrt(2)`

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

The roots of the equation 4x^2-2sqrt(5)x+1=0,a r e

Roots of the equation 3x^2 -6x+4=0 are alpha and beta then find the value of alpha^2 beta + alpha beta^2

IF alpha and beta be the roots of the equation ax^2+bx+c=0 , find the values of alpha^2+beta^2

IF alpha and beta be the roots of the equation x^2+3x+4=0 , find the equation whose roots are (alpha+beta)^2 and (alpha+beta)^2

If alpha and beta be the roots of the equation x^2+3x+4=0 find the equation whose roots are (alpha+beta)^2 and (alpha-beta)^2 .

IF alpha and beta be the roots of the equation 2x^2+x+1=0 find the equation whose roots are alpha^2/beta and beta^2/alpha

If alpha,beta,gamma,delta are the roots of the equation x^4-K x^3+K x^2+L x+m=0,w h e r eK ,L ,a n dM are real numbers, then the minimum value of alpha^2+beta^2+gamma^2+delta^2 is a. 0 b. -1 c. 1 d. 2

IF alpha and beta are the roots of the equation x(x-3)=4, find the value of alpha^2+beta^2 .

Two roots of the equation ax^2 +bx +c=0 is alpha,beta then find the value of alpha^2 + beta^2

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

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If one root x^2-x-k=0 is square of the other, then k= a.2+-sqrt(5)...

    Text Solution

    |

  2. If z1, z2 are complex number such that (2z1)/(3z2) is purely imaginary...

    Text Solution

    |

  3. If alpha,a n dbeta be the roots of the equation x^2+p x-1//2p^2=0,w h ...

    Text Solution

    |

  4. If z1,z2,z3 are complex numbers such that 2/z1=1/z2 + 1/z3, show that ...

    Text Solution

    |

  5. Find the range of f(x)(x^2-x+1)/(x^2+x+1)

    Text Solution

    |

  6. If ((3-z1)/(2-z1))((2-z2)/(3-z2))=k(k >0) , then prove that points A(z...

    Text Solution

    |

  7. x^2-x y+y^2-4x-4y+16=0 represents a. a point b. a circle c. ...

    Text Solution

    |

  8. If (x+i y)^5=p+i q , then prove that (y+i x)^5=q+i pdot

    Text Solution

    |

  9. If alpha,beta are the nonzero roots of a x^2+b x+c=0 and alpha^2,beta^...

    Text Solution

    |

  10. Find real theta such that (3+2isintheta)/(1-2isintheta) is purely real...

    Text Solution

    |

  11. If the roots of the equation a x^2+b x+c=0 are of the form (k+1)/k and...

    Text Solution

    |

  12. Prove that tan(iloge((a-ib)/(a+ib)))=(2ab)/(a^2-b^2) (where a, b in ...

    Text Solution

    |

  13. If alpha,beta are the roots of a x^2+b x+c=0a n dalpha+h ,beta+h are t...

    Text Solution

    |

  14. Find the real part of (1-i)^(-i)dot

    Text Solution

    |

  15. The equation (x^2+x+1)^2+1=(x^2+x+1)(x^2-x-5) for x in (-2,3) will h...

    Text Solution

    |

  16. Convert of the complex number in the polar form: 1-i

    Text Solution

    |

  17. If alpha,beta are the roots of a x^2+c=b x , then the equation (a+c y)...

    Text Solution

    |

  18. If z=r e^(itheta) , then prove that |e^(i z)|=e^(-r sintheta)

    Text Solution

    |

  19. If the roots of the equation x^2+2a x+b=0 are real and distinct and th...

    Text Solution

    |

  20. Z1!=Z2 are two points in an Argand plane. If a|Z1|=b|Z2|, then prove t...

    Text Solution

    |