Home
Class 12
MATHS
Find the sum of the roots (real or compl...

Find the sum of the roots (real or complex) of the equation `x^2001 + (1/2-x)^2001=0` .

A

`2000`

B

`2001`

C

`1000`

D

`500`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` `x^(2001)-["^(2001)C_(0)x^(2001)-^(2001)C_(1)x^(2000)*(1)/(2)+^(2001)C_(2)x^(1999)*(1)/(4)...]=0`
`:. ^(2001)C_(1)x^(2000)*(1)/(2)-^(2001)C_(2)x^(1999)*(1)/(4)...=0`
sum of the roots `=^(2001)C_(2)*(1)/(4)*(2)/("^(2000)C_(1))=(2001*2000)/(4*2001)=500`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE|Exercise Multiple Correct Answer|4 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Comprehension|11 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise JEE Previous Year|16 Videos

  • AREA UNDER CURVES

    CENGAGE|Exercise Question Bank|20 Videos

  • BINOMIAL THEORM

    CENGAGE|Exercise Question Bank|31 Videos

Similar Questions

Explore conceptually related problems

Sum of the real roots of the equation x^(2)+5|x|+6=0

The sum of all real roots of the equation |x-3|^(2)+|x-3|-2=0

Find the absolute value of the difference of the real roots of the equation x^(2)-2^(2010)x+|x-2^(2009)|+2(2^(4017)-1)=0

The positive real root of the equation 64 x^(2) - 1 = 0 is

The sum of all the real roots of the equation |x-2|^(2)+|x-2|-2=0 is

The sum of the real roots of the equation 2x-3=sqrt(2x^(2)-2x+21) is

CENGAGE-BINOMIAL THEOREM-Single correct Answer
  1. The coefficient of x^70 in the product (x-1)(x^2-2)(x^3-3)....(x^12-12...

    Text Solution

    |

  2. Given (1-x^(3))^(n)=sum(k=0)^(n)a(k)x^(k)(1-x)^(3n-2k) then the value ...

    Text Solution

    |

  3. Find the sum of the roots (real or complex) of the equation x^2001 + (...

    Text Solution

    |

  4. If the 4^(th) term of {sqrt(x^((1)/(1+log(10)x)))+root(12)(x)}^(6) is ...

    Text Solution

    |

  5. The number of distinct terms in the expansion of (x+y^(2))^(13)+(x^(2)...

    Text Solution

    |

  6. The value of sum(r=1)^n(sum(p=0)^(r-1) ^nCr ^rCp 2^p) is equal to

    Text Solution

    |

  7. If in the expansion of (x^(3)-(2)/(sqrt(x)))^(n) a term like x^(2) exi...

    Text Solution

    |

  8. In (3 3+1/(3 3))^n if the ratio of 7th term from the beginning to the ...

    Text Solution

    |

  9. The number of distinct terms in the expansion of is (x^(3)+(1)/(x^(3))...

    Text Solution

    |

  10. If r^[th] and (r+1)^[th] term in the expansion of (p+q)^n are equal, ...

    Text Solution

    |

  11. If (3+asqrt2)^100+(3+bsqrt2)^100=7+5sqrt2 number of pairs (a, b) for...

    Text Solution

    |

  12. The middle term in the expansion of (1-3x+3x^2-x^3)^(2n) is

    Text Solution

    |

  13. The algebraically second largest term in the expansion of (3-2x)^(15) ...

    Text Solution

    |

  14. If 6^(th) term in the expansion of ((3)/(2)+(x)/(3))^(n) is numericall...

    Text Solution

    |

  15. Let (5 + 2sqrt6)^n= p+ f, where n in N and p in N and 0ltflt1, then th...

    Text Solution

    |

  16. The sum of last 3 digits of 3^100 is

    Text Solution

    |

  17. The remainder when 27^(10)+7^(51) is divided by 10

    Text Solution

    |

  18. Consider the sequence ('^(n)C(0))/(1.2.3),("^(n)C(1))/(2.3.4),('^(n)C(...

    Text Solution

    |

  19. If P(n) denotes the product of all the coefficients of (1+x)^(n) and 9...

    Text Solution

    |

  20. If N is a prime number which divides S=^(39)P(19)+^(38)P(19)+^(37)P(19...

    Text Solution

    |