Home
Class 12
MATHS
Let alpha,beta,gamma are the real roots ...

Let `alpha,beta,gamma` are the real roots of the equation `x^3+a x^2+b x+c=0(a ,b ,c in Ra n da!=0)dot` If the system of equations `(inu ,v ,a n d w)` given by `alphau+betav+gammaw=0` `betau+gammav+alphaw=0` `gammau+alphav+betaw=0` has non-trivial solutions then the value of `a^2//b` is ________.

A

0

B

3

C

5

D

1

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • JEE MAIN 2021

    JEE MAINS PREVIOUS YEAR|Exercise MATHEMATICS SECTION B|20 Videos
  • JEE MAIN 2021

    JEE MAINS PREVIOUS YEAR|Exercise Mathematic section A|20 Videos
  • JEE MAIN 2021

    JEE MAINS PREVIOUS YEAR|Exercise MATHEMATICS (SECTION B)|30 Videos
  • JEE MAIN

    JEE MAINS PREVIOUS YEAR|Exercise QUESTION|1 Videos
  • JEE MAIN 2022

    JEE MAINS PREVIOUS YEAR|Exercise Question|454 Videos

Similar Questions

Explore conceptually related problems

Let alpha,beta,gamma are the real roots of the equation x^(3)+ax^(2)+bx+c=0(a,b,c in R and a!=0) If the system of equations (inu,v,andw) given by alpha u+beta v+gamma w=0 beta u+gamma v+alpha w=0gamma u+alpha v+beta w=0 has non-trivial solutions then the value of a^(2)/b is

Let alpha, beta and gamma are the roots of equation x^(3) + ax^(2) + bx + c = 0 (a, b, c in R, a != 0) . If system of equations alphax + betay + gammaz = 0 betax + gammay + alphaz = 0 gammax + alphay + betaz = 0 has non trivial solution then the value of ((a^2)/(b)) is :

Let alpha ,beta and gamma be the roots of the equations x^(3) +ax^(2)+bx+ c=0,(a ne 0) . If the system of equations alphax + betay+gammaz=0 beta x +gamma y+ alphaz =0 and gamma x =alpha y + betaz =0 has non-trivial solution then

Let a, b, c be non-zero real roots of the equation x^(3)+ax^(2)+bx+c=0 . Then

Let system of equation alphau+betav+gammaw=0 , betau+gammav+alphaw=0 , gammau+alphav+betaw=0 has non trial solution and alpha, beta, gamma are distinct root x^3+ax^2+bx+c=0 then find value of a^2/b

Let alpha , beta be the roots of the equation (x-a) (x-b) = c , cne 0 , then find the roots of the equation (x - alpha) (x -beta) + c = 0

If alpha and beta ( alpha

If alpha and beta are the roots of the equation x^(2)-ax+b=0 and A_(n)=alpha^(n)+beta^(n)

JEE MAINS PREVIOUS YEAR-JEE MAIN 2021-MATHEMATICS SECTION A
  1. The equation of one of the straight lines which passes through the poi...

    Text Solution

    |

  2. The number of integral values of m so the abscissa of point of interse...

    Text Solution

    |

  3. Let alpha,beta,gamma are the real roots of the equation x^3+a x^2+b x+...

    Text Solution

    |

  4. The real valued function f(x)=(cosec^(-1)x)/(sqrt(x-[x])), where [x] d...

    Text Solution

    |

  5. The value of is equal to

    Text Solution

    |

  6. Let A+2B=[(1,2,0),(6,-1,3),(-5,3,1)] and 2A-B=[(2,-1,5),(2,-1,6),(0,1,...

    Text Solution

    |

  7. If lim(xto0)(sin^(-1)x-tan^(-1)x)/(3x^3) is equal to L, then the value...

    Text Solution

    |

  8. A vector veca has components 3p and 1 with rrespect to a rectangular c...

    Text Solution

    |

  9. If alpha,beta are natural numbers such that 100^(alpha)-199beta=(100)(...

    Text Solution

    |

  10. If the equation aabsz^2+bar(baralphaz+alphabarz)+d=0 represents a ci...

    Text Solution

    |

  11. The differential equation satisfied by the system of parabolas y^2=4a(...

    Text Solution

    |

  12. Let (1+x+2x^2)^20=a0+a1x+a2x^2+....+a40x^40. " Then, "a1+a3+a5.....+a3...

    Text Solution

    |

  13. The sum of all the 4-digit distinct numbers that can be formed with th...

    Text Solution

    |

  14. If the functions are defined as f(x)=sqrtx and g(x) = sqrt(1-x), then ...

    Text Solution

    |

  15. For the four circles M, N, O and P, following four equations are given...

    Text Solution

    |

  16. If x, y, z are in arithmetic progression with common difference d, x n...

    Text Solution

    |

  17. Tha value of the limit lim(theta to 0) (tan(pi cos^(2)theta))/(sin (2p...

    Text Solution

    |

  18. Let S(1), S(2) and S(3) be three sets defined as S(1)={z in CC:|z-1|...

    Text Solution

    |

  19. Let L be a tangent line to the parabola y^(2)=4x - 20 at (6, 2). If L ...

    Text Solution

    |

  20. Let the tangent to the circle x^(2) + y^(2) = 25 at the point R(3, 4) ...

    Text Solution

    |