Home
Class 11
MATHS
If alpha be a root of the quadratic equa...

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

Promotional Banner

Topper's Solved these Questions

  • Kalidhan Institution, Question Paper

    UNITED BOOK HOUSE|Exercise Exercise |23 Videos

  • MODEL QUESTION PAPERS-SET 1

    UNITED BOOK HOUSE|Exercise EXERCISE|50 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 is a root of the equation 4x^2+2x-1=0, then prove that 4alpha^3-3alpha is the other root.

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

Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic equation x^2-p x+1=0. a n dalpha^2,beta are the roots of quadratic equation x^2-q x+8=0, then find p ,q,alpha,betadot

If alpha,beta are the roots of the quadratic equation x^2+px+q=0 , then the values of alpha^3+beta^3 and alpha^4+alpha^2beta^2+beta^4 are respectively

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 alphaandbeta be the roots of the quadratic equation 2x^(2)+2x-3=0 , then find the values of alpha+beta+1

If alpha,beta are the roots of the quadratic equation x^(2)+px+q=0 ,then the values of alpha^(3)+beta^(3)andalpha^(4)+alpha^(2)beta^(2)+beta^(4) are respectively .

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

If the roots of the quadratic equation 5x^2 - 2x - 3 = 0 be alpha and beta , find the value of (1)/(alpha)+(1)/(beta) .

UNITED BOOK HOUSE-MCQ-EXERCISE
  1. Two balls are drawn at random from a bag containing 6 white and 4 blac...

    Text Solution

    |

  2. If the circles x^2+y^2+2ax+c^2=0and x^2+y^2+2by+c^2=0touch each other,...

    Text Solution

    |

  3. If acosphi=b costheta,show that a tantheta+b tanphi=(a+b)tan((theta+ph...

    Text Solution

    |

  4. If (cot(alpha-beta))/cotalpha+(cos^2gamma)/(cos^2alpha)=1show that tan...

    Text Solution

    |

  5. Solve :cos^3xcos3x+sin^3xsin3x=0

    Text Solution

    |

  6. In any triangle ABC If sinA : sinB: sinC=4:5:6,then prove that cos A ...

    Text Solution

    |

  7. Find the domain of definition of the function defined by f(x)=1/loge(2...

    Text Solution

    |

  8. Solve :barz=iz^2(z being a complex number)

    Text Solution

    |

  9. if x be real, show that the value of (2x^2-2x+4)/(x^2-4x+3)cannot lie ...

    Text Solution

    |

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

    Text Solution

    |

  11. solve : |x+2|/x<3where x in Rand x!=0

    Text Solution

    |

  12. Show that there are 136 ways of selecting 4 letters from the word EXAM...

    Text Solution

    |

  13. If the coefficient of-four successive termsin the expansion of (1+x)^n...

    Text Solution

    |

  14. If s1,s2,s3are thesums of n natural numbers, theirsquares, their cubes...

    Text Solution

    |

  15. Find the sum upto n terms : 12+14+24+58+164+….

    Text Solution

    |

  16. Find the equation of the parabola whose co-ordinate of vertex is (-2, ...

    Text Solution

    |

  17. If (alpha+beta)and (alpha-beta)are the eccentric angles of the points ...

    Text Solution

    |

  18. The foci of the ellipse x^2/25+y^2/9=1 coincide with a hyperbola. If e...

    Text Solution

    |

  19. The equation of auxiliary circle of the ellipse 16x^(2)+25y^(2)+32x-10...

    Text Solution

    |

  20. Find the area of the parabola y^(2) = 4ax bounded by its latus rectum.

    Text Solution

    |