Home
Class 12
MATHS
If f(x) is is a polynomial of degree...

If f(x) is is a polynomial of degree n with rational coefficients and `1 +2 I ,2 - sqrt(3) ` and 5 are roots of f(x) =0 then the least value of n is

A

5

B

4

C

3

D

6

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    AAKASH SERIES|Exercise EXERCISE-III|46 Videos

  • THEORY OF EQUATIONS

    AAKASH SERIES|Exercise EXERCISE-I|47 Videos

  • SYSTEM OF CIRCLES

    AAKASH SERIES|Exercise EXERCISE 2.2|22 Videos

  • TRANSFORMATIONS AND INDENTITIES

    AAKASH SERIES|Exercise PRACTIVE EXERCISE|36 Videos

Similar Questions

Explore conceptually related problems

If (x) is a polynomal of degree n with rational coeficients and 1 + 2i, 2 - sqrt(3) and 5 are three roots of f(x) = 0 , then the least value of n is

Form the polynomial equation with rational coefficients whose roots are i-sqrt(5)

The equation of lowest degree with rational coefficient having a root sqrt(3) + sqrt(2) is

The equaiton of lowest degree with rational coefficients having a roots sqrt(3) + sqrt(2) is

Form the polynomial equation with rational coefficients whose roots are 4sqrt(3),5+2i

Find the polynomial with rational coefficients and whose roots are 0,1,-3//2,5//2

Form the polynomial with rational coefficients whose roots are 1+ 5i ,5-i

AAKASH SERIES-THEORY OF EQUATIONS-EXERCISE-II
  1. If f(x) = 2x^4 - 13 x^2 + ax +b is divisible by x^2 -3x +2 the...

    Text Solution

    |

  2. Let a ne 0 and p(x ) be a polynomial of degree greater than ...

    Text Solution

    |

  3. If f(x) is is a polynomial of degree n with rational coefficien...

    Text Solution

    |

  4. If (1 + I sqrt(3))/(2) is a root of the equation x^4-x^3 +x-1=0 ...

    Text Solution

    |

  5. If the roots of the equation x^4 - 10x^3 +50 x^2 - 130 x + 16...

    Text Solution

    |

  6. If 1,2,3 and 4 are the roots of the equation x^4 + ax^3 + bx^2 +...

    Text Solution

    |

  7. If sqrt(3) +1 is a root of the equation 3x^3 + ax^2 + bx +12 =0...

    Text Solution

    |

  8. If the roots of x^3 - 9x^2 +kx +l=0 are in A.P with common dif...

    Text Solution

    |

  9. The roots of the equation x^(3) - 14x^(2) + 56x- 64 = 0 are in …… pr...

    Text Solution

    |

  10. The roots of 48x^3 - 44 x^2 + 12 x -1=0 are in

    Text Solution

    |

  11. The difference between two roots of the equation x^3 -13 x^2 + 15 ...

    Text Solution

    |

  12. If two roots of x^3 - 9x^2 + 14 x +24 =0 are in the ratio 3:2 t...

    Text Solution

    |

  13. If - 1 + i is a root of x^(4) + 4x^(3) + 5x^(2) + 2x + k = 0 then k =

    Text Solution

    |

  14. If the roots of x^4 - 8x^3 + 14 x^2 + 8x - 15=0 are in A.P t...

    Text Solution

    |

  15. If the roots of x^4 +5x^3 - 30 x^2 - 40 x+64=0 are in G.P then...

    Text Solution

    |

  16. If the sum of two of the roots of x^4 -2x^3 -3x^2 +10 x-10=0 i...

    Text Solution

    |

  17. the roots of the equation x^4 -6x^3 + 18x^2- 30 x +25 =0 are of...

    Text Solution

    |

  18. Assertion (A) : If 1,2,3 are the roots of ax^3 + bx ^2 +cx +d=0 ...

    Text Solution

    |

  19. If the product of two of the roots of x^4 - 5x^3 + 5x^2 + 5x -6=...

    Text Solution

    |

  20. The equation x^3 -3qx +2r =0 has a repeated root then

    Text Solution

    |