Home
Class 11
MATHS
If alpha,beta are the roots of the equat...

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`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise All Questions|365 Videos
  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

Similar Questions

Explore conceptually related problems

If alpha,beta are the roots of the equation, x^2-2x+3=0, find the equation whose roots are alpha^3-3alpha^2+5alpha-1a n dbeta^3-beta^2+beta+5.

If alpha,beta are the roots of the equation x^(2)-3x+4=0 , then the equation whose roots are (alpha-2)/(alpha+2),(beta-2)/(beta+2) is

If alpha, beta are the roots of the equation 2x^(2) - 3x - 6 = 0 , find the equation whose roots are alpha^(2) + 2 and beta^(2) + 2 .

If alpha, beta are the roots of the equation x^(2)+7x+12=0 , then the equation whose roots are (alpha+beta)^(2) and (alpha-beta)^(2) is

If alpha and beta are the roots of the equation 2x^(2)+3x+2=0 , find the equation whose roots are alpha+1 and beta+1 .

If alpha and beta are the roots of the equation x^(2)+x-7=0 , form the equation whose roots are alpha^(2) and beta^(2) .

If alpha, beta are roots of the equation ax^2 + bx + c = 0 then the equation whose roots are 2alpha + 3beta and 3alpha + 2beta is

If alpha,beta are the roots of the equation 2x^2+2(a+b)x+a^2+b^2=0 , then find the equation whose roots are (alpha+beta)^2a n d(alpha-beta)^2

IF alpha , beta are the roots of the equation ax^2+ bx +c=0 then the quadratic equation whose roots are alpha + beta , alpha beta is

If alpha, beta are the roots of x^(2)+x+1=0 , then the equation whose roots are alpha^(5), beta^(5) is

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Let a,b and c be real numbers such that 4a+2b+c=0 and ab gt 0.Then t...

    Text Solution

    |

  2. If |z|<=1,|w|<=1, then show that |z- w|^2<=(|z|-|w|)^2+(argz-argw)^2

    Text Solution

    |

  3. If alpha,beta are the roots of the equation x^2-2x+3=0 obtain the equa...

    Text Solution

    |

  4. For complex numbers z and w, prove that |z|^2w- |w|^2 z = z - w, if...

    Text Solution

    |

  5. If alpha,beta are the roots of the equation a x^2+b x+c=0, then the va...

    Text Solution

    |

  6. Let z1 \and\ z2 be the roots of the equation z^2+p z+q=0, where the co...

    Text Solution

    |

  7. If a in (-1,1), then roots of the quadratic equation (a-1)x^2+a x+sqrt...

    Text Solution

    |

  8. The maximum value of |a r g(1/(1-z))| for |z|=1,z!=1 is given by.

    Text Solution

    |

  9. If one root is square of the other root of the equation x^2+p x+q=0, t...

    Text Solution

    |

  10. If z^4+1=sqrt(3)i (A) z^3 is purely real (B) z represents the vertic...

    Text Solution

    |

  11. Let alpha,beta be the roots of the quadratic equation a x^2+b x+c=0 an...

    Text Solution

    |

  12. If x=a+bi is a complex number such that x^2=3+4i and x^3=2+11i, where...

    Text Solution

    |

  13. Let alpha,beta be the roots of x^2-x+p=0a n dgamma,delta are roots of ...

    Text Solution

    |

  14. If the difference between the roots of the equation x^2+""a x""+""1...

    Text Solution

    |

  15. If f(x)=x^2+2b x+2c^2 and g(x)= -x^2-2c x+b^2 are such that min f(x...

    Text Solution

    |

  16. Let z be a complex number such that the imaginary part of z is nonzero...

    Text Solution

    |

  17. For the equation 3x^2+p x+3=0,p >0, if one of the root is square of th...

    Text Solution

    |

  18. Let z,w be complex numbers such that barz+ibarw=0 and arg zw=pi Then a...

    Text Solution

    |

  19. Let f(x)=(1+b^2)x^2+2b x+1 and let m(b) be the minimum value of f(x)do...

    Text Solution

    |

  20. For any two complex numbers z1 and z2, , prove that Re (z1 z2) = Re ...

    Text Solution

    |