Home
Class 12
MATHS
Let alpha\ &\ beta be the roots of equat...

Let `alpha\ &\ beta` be the roots of equation `a x^2+b x+c=0\ a n d S_n=alpha^n+beta^nfor\ ngeq1.` Evaluate the value of the determinant `|3 1+S_1 1+S_2 1+S_1 1+S_2 1+S_3 1+S_2 1+S_3 1+S_4|`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPOUND ANGLES

    ALLEN|Exercise EX -JA|8 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    ALLEN|Exercise All Questions|147 Videos

Similar Questions

Explore conceptually related problems

Let alpha and beta be the roots of the equation 5x^2+6x-2=0 . If S_n=alpha^n+beta^n, n=1,2,3.... then

Let alpha,beta , be the roots of the equation x^2+x-1=0 . Let S_n=alpha^n+beta^n "for" n ge 1 . Evaluate the determinant |{:(3,1+s_1,1+s_2),(1+s_1,1+s_2,1+s_3),(1+s_2,1+s_3,1+s_4):}|

If alpha, beta are roots of equation x^(2)-4x-3=0 and s_(n)=alpha^(n)+beta^(n), n in N then the value of (s_(7)-4s_(6))/s_(5) is

If alpha,beta are the roots of the equation ax^2+bx+c=0 and S_n=alpha^n+beta^n then evaluate |[3, 1+s_1, +s_2] , [1+s_1, 1+s_2, 1+s_3] , [1+s_2, 1+s_3, 1+s_4]|

If alpha , beta are the roots of the equation ax^(2)+bx+c=0 and S_(n)=alpha^(n)+beta^(n) , then aS_(n+1)+bS_(n)+cS_(n-1)=(n ge 2)

if alpha , beta be roots of equation 375 x^2 -25 x -2 = 0 and s_n = alpha^n + beta^n then lim_(n->oo) (sum_(r=1)^n S_r) = .......

If alphaa n dbeta are the roots of ax^2+bx+c=0a n dS_n=alpha^n+beta^n, then a S_(n+1)+b S_n+c S_(n-1)=0 and hence find S_5dot

If alpha, beta be the real roots of ax^2+bx+c=0 , and s_n=alpha^n + beta^n then prove that as_n + bs_(n-1)+cs_(n-2)=0 .for all n in N .

If alpha and beta are the zeros of the quadratic polynomial p(s)=3s^2-6s+4 , find the value of alpha/beta+beta/alpha+2(1/alpha+1/beta)+3alphabeta .

If S_n denotes the sum of first n natural number then S_1 + S_2x + S_3 x^2 +……+S_n x^(n-1) + ……oo terms =

ALLEN-DETERMINANTS-All Questions
  1. If |{:(3^(2)+k,4^(2),3^(2)+3+k),(4^(2)+k,5^(2),4^(2)+4+k),(5^(2)+k,6^...

    Text Solution

    |

  2. Prove that |{:(a, a, x), (m, m, m), (b, x, b):}|=m(x-a)(x-b)

    Text Solution

    |

  3. Let alpha\ &\ beta be the roots of equation a x^2+b x+c=0\ a n d Sn=al...

    Text Solution

    |

  4. Prove that |1alphaalpha^2alphaalpha^2 1alpha^2 1alpha|=-(1-alpha^3)^2d...

    Text Solution

    |

  5. Find the nature of solution for the given system of equation: x+2y+3...

    Text Solution

    |

  6. Find the value of lambda if the following equations are consistent ...

    Text Solution

    |

  7. If the system of equation x+lambday+1=0,\ lambdax+y+1=0\ &\ x+y+lambda...

    Text Solution

    |

  8. The value of the determinant |[a-b,b+c, a], [b-a, c+a, b], [c-a, a+b...

    Text Solution

    |

  9. If |[sin2x,cos^2x,cos4x],[cos^2x,cos2x,sin^2x],[cos^4x,sin^2x,sin2x]|=...

    Text Solution

    |

  10. The value of the determinant |-a b c a-b c a b-c| is equal to- 0 b. (a...

    Text Solution

    |

  11. For any "Delta"A B C the value of determinant |sin^2\ \ A cot A1sin^2B...

    Text Solution

    |

  12. If Dp=|p 15 8p^2 35 9p^3 25 10|,\ t h e n\ D1+D2+D3+D5 is equal to- a....

    Text Solution

    |

  13. If A+B+C=pi,\ t h e n\ |"sin"(A+B+C)s in B cos C-s in B0t a n A"cos"(A...

    Text Solution

    |

  14. The number of real values of x satisfying |(x,3x+2,2x-1),(2x-1,4x,3x+1...

    Text Solution

    |

  15. If a ,\ b ,\ c are pth, qth and rth terms of a GP, the |loga p1logb q1...

    Text Solution

    |

  16. If a1, a2 an ,\ a(n+1) are in GP and a1>0AAI ,\ t h e n |loganloga(n+2...

    Text Solution

    |

  17. If p x^4+q x^3+r x^2+s x+t=|x^2+3xx-1x+3x+1 2-xx-3x-3x+4 3x| then t is...

    Text Solution

    |

  18. For positive numbers x ,\ y\ a n d\ z the numerical value of the deter...

    Text Solution

    |

  19. If a, b,c> 0 and x,y,z in RR then the determinant |((a^x+a^-x)^2,(a...

    Text Solution

    |

  20. For determinant |((a^2+b^2)/c,c,c),(a,(b^2+c^2)/a,a),(b,b,(c^2+a^2)/b...

    Text Solution

    |