Home
Class 12
MATHS
Let alpha=(-1+isqrt(3))/2 and a=(1+alpha...

Let `alpha=(-1+isqrt(3))/2` and `a=(1+alpha)sum_(k=0)^(100) alpha^(2k),b=sum_(k=0)^(100) alpha^(3k)` . If a and b are roots of quadratic equation then quadratic equation is

A

`X^(2)-102X+101=0`

B

`X^(2)+102X+101=0`

C

`X^(2)+101+100=0`

D

`X^(2)=101X+100=0`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • JEE MAIN

    JEE MAINS PREVIOUS YEAR ENGLISH|Exercise MATHEMATICS|121 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    JEE MAINS PREVIOUS YEAR ENGLISH|Exercise All Questions|2 Videos

  • JEE MAINS

    JEE MAINS PREVIOUS YEAR ENGLISH|Exercise All Questions|445 Videos

Similar Questions

Explore conceptually related problems

Let alpha=(-1+isqrt3)/2 . If a =(1 +alpha^2)underset(k-0)overset(100)(Sigma)alpha^k and b = underset(k-0)overset(10)(Sigma)alpha^(6k) , , then a and b are the roots of the quadratic equation : A. x^2 - 102x + 11 =0 B. x^2 + 12x + 11 =0 C. x^2 - 12 x - 11 =0 D. x^2 - 12 x+ 11=0

If alpha and beta are the roots of a quadratic equation such that alpha+beta=2, alpha^4+beta^4=272 , then the quadratic equation is

If roots of quadratic equation x ^2 −kx+4=0 then k will be a. 2 b 1 c. 3 d. 4

Let alpha, beta are the roots of the equation x^(2)+x+1=0 , then alpha^3-beta^3

If alpha and beta are the roots of the quadratic equation ax^(2)+bx+1 , then the value of 2alpha^(2)beta^(2) is

If alpha and beta are the roots of the quadratic equation ax^(2)+bx+1 , then the value of (1)/(alpha)+(1)/(beta) is

If alpha and beta are the roots of the quadratic equation ax^(2)+bx+1 , then the value of (1)/(alpha beta)+(alpha+beta) is

If alpha != beta but, alpha^(2) = 4alpha - 2 and beta^(2) = 4beta - 2 then the quadratic equation with roots (alpha)/(beta) and (beta)/(alpha) is

Two different real numbers alpha and beta are the roots of the quadratic equation ax ^(2) + c=0 a,c ne 0, then alpha ^(3) + beta ^(3) is:

JEE MAINS PREVIOUS YEAR ENGLISH-JEE MAIN-MATH
  1. If a hyperbola has vertices (±6, 0) and P(10, 16) lies on it, then the...

    Text Solution

    |

  2. It the 10^(th) term of an A. P. is 1/20 and its 20^(th) term is 1/10, ...

    Text Solution

    |

  3. Let A=[[2,2],[9,4]] and I=[[1,0],[0,1]] then value of 10 A^(-1) is-

    Text Solution

    |

  4. Let alpha=(-1+isqrt(3))/2 and a=(1+alpha)sum(k=0)^(100) alpha^(2k),b=s...

    Text Solution

    |

  5. lambda x + 2y + 2z = 5, 2lambda x + 3y + 5z = 8, 4x + lambda y + 6z =...

    Text Solution

    |

  6. Let veca=hati-2hatj+hatkand vecb=hati-hatj+hatk be two vectors. If vec...

    Text Solution

    |

  7. Let f(x) = (x[x])/(x^2+1) : (1, 3) rarr R then range of f(x) is (where...

    Text Solution

    |

  8. lim(x rarr 0)(int0^x tsin(10t)dt)/x is equal to

    Text Solution

    |

  9. Normal at (2, 2) to curve x^2 + 2xy – 3y^2 = 0 is L. Then perpendicula...

    Text Solution

    |

  10. Let A and B two events such that the probability that exactly one of t...

    Text Solution

    |

  11. The differential equation of the family of curves, x^(2)=4b(y+b),b in ...

    Text Solution

    |

  12. Let P be the set of points (x, y) such that x^2 le y le – 2x + 3. Then...

    Text Solution

    |

  13. Image of (1, 2, 3) w.r.t a plane is (-7/3,-4/3,-1/3) then which of th...

    Text Solution

    |

  14. Mean and variance of 20 observation are 10 and 4. It was found, that i...

    Text Solution

    |

  15. Let coefficient of x^4 and x^2 in the expansion of (x+sqrt(x^2-1))^6+(...

    Text Solution

    |

  16. Solution set of 3^x (3^x –1) + 2 = |3^x –1| + |3^x – 2| contains

    Text Solution

    |

  17. If I=int(1)^(2)(dx)/(sqrt(2x^(3)-9x^(2)+12x+4)), then

    Text Solution

    |

  18. Let f(x) is a three degree polynomial for which f ' (–1) = 0, f '' (1)...

    Text Solution

    |

  19. If sqrt2(sin alpha)/(sqrt(1+cos2 alpha))=1/7 and sqrt((1-cos2beta)/2)=...

    Text Solution

    |

  20. Let the line y = mx intersects the curve y^2 = x at P and tangent to y...

    Text Solution

    |