Home
Class 11
MATHS
If alpha is a root of the equation 4x^2...

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

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

IF alpha be a root of the quadratic equation 4x^2+2x-1=0 , Let prove that 4alpha^3-3alpha is the other root.

If alpha be a root of the quadratic equaiton 4x^2+2x-1=0 .Prove that 4alpha^3-3alpha is the other root.

If one root of the equation (alpha-4)x^2+2x+1=0 is 1, then alpha =

IF alpha be a root of the equation 3x^2-4x+5=0 , prove that 2alpha^2 is a root of the equation 9x^2+28x+100=0 .

If alpha is a root of 4x^2+2x-1 =0, then the other root is

If alpha,beta are the roots of the equation x^2-2x+3=0 obtain the equation whose roots are alpha^3-3alpha^2+5alpha-2 and beta^3-beta^2+beta=5

IF one root of the quadratic equation x^2-x-1=0 is alpha , prove that its other root is alpha^3-3alpha .

IF alpha,beta be the roots of the equation x^2+px+q=0 , show that 1/(alpha+beta) and 1/alpha+1/beta are the roots of pqx^2+(p^2+q)x+p=0

If alpha, beta be the roots of the equation x^(2)+x+1=0 , the value of alpha^(4)beta^(4)-alpha^(-1)beta^(-1) is

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

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If the equation (a-5)x^2+2(a-10)x+a+10=0 has roots of opposite sign, t...

    Text Solution

    |

  2. If alphaa n dbeta are the roots of ax^2+bx+c=0a n dSn=alpha^n+beta^n,...

    Text Solution

    |

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

    Text Solution

    |

  4. If both the roots of x^2-a x+a=0 are greater than 2, then find the val...

    Text Solution

    |

  5. If (y^2-5y+3)(x ^2+x+1)<2x for all x in R , then find the interval in...

    Text Solution

    |

  6. Find the values of 'a' which 4^t-(a-4)2^t+9/4alt0,foralltin(1,2)

    Text Solution

    |

  7. Find the number of positive integral values of k for which kx ^(2) +(k...

    Text Solution

    |

  8. If x^2+2ax+a lt 0 AA x in [1, 2] then find set of all possible values ...

    Text Solution

    |

  9. Given that a ,b ,c are distinct real numbers such that expressions a x...

    Text Solution

    |

  10. Find the number of quadratic equations, which are unchanged by squarin...

    Text Solution

    |

  11. Solve the following: (sqrt(x^2-5x+6)+sqrt(x^2-5x+4))^(x/2)+(sqrt(x^2-...

    Text Solution

    |

  12. Show that the equation A^2/(x-a)+B^2/(x-b)+C^2/(x-c)+.....+H^2/(x-h)=...

    Text Solution

    |

  13. Find the values of a if x^2-2(a-1)x+(2a+1)=0 has positive roots.

    Text Solution

    |

  14. If alphaa n dbeta,alphaa n dgamma,alphaa n ddelta are the roots of th...

    Text Solution

    |

  15. If alphabeta the roots of the equation x^2-x-1=0 , then the quadratic...

    Text Solution

    |

  16. If a(p+q)^2+2b p q+c=0 and a(p+r)^2+2b p r+c=0 (a!=0) , then which one...

    Text Solution

    |

  17. If alpha1,alpha2 are the roots of equation x ^2-p x+1=0a n dbeta1,bet...

    Text Solution

    |

  18. Suppose A, B, C are defined as A=a^2b+a b^2-a^2c-a c^2 , B=b^2c+b c^2-...

    Text Solution

    |

  19. The integral value of m for which the root of the equation m x^2+(2m-1...

    Text Solution

    |

  20. If b1. b2=2(c1+c2) then at least one of the equation x^2+b1x+c1=0 and ...

    Text Solution

    |