Home
Class 12
MATHS
If alpha, beta are the roots of a x^(2)+...

If alpha, beta are the roots of a `x^(2)+b x+c=0` and `A_(n)=alpha^(n)+beta^(n)`, then, `a A_(n+2)+b A_(n+1)+c A_(n)=`

A

1: 0

B

2: 1

C

3: `a+b+c`

D

4: a b c

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • PROGRESSIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|97 Videos

  • SETS,RELATIONS AND FUNCTIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|285 Videos

Similar Questions

Explore conceptually related problems

If alpha, beta are the roots of x^(2)-a x+b=0 and A_(n)='alpha'^(n)+beta^(n) , then A_(n+1)=

If alpha, beta are roots of 375x^(2) - 25x - 2 = 0 and s_(n) = alpha^(n) + beta^(n), then underset(n rarr infty) sum_(r = 1)^(n) S_(r) is :

If alpha , beta are roots of 375 x^(2) - 25x - 2 = 0 and s_(n) = alpha^(n) + beta^(n) , then underset(n rarr infty)(lim) sum_(r= 1)^(n) s_(r) is :

Let alpha and beta be the roots of equation x^(2) - 6x -2 = 0 . If a_(n) = a^(n) - beta^(n), for n ge l , then the value of (a_(10) - 2 a_(8))/(2 a_(9)) is equal to :

Let alpha and beta be the roots of x^(2) -6x - 2 =0 , with alpha gt beta . If a_(n) = alpha^(n) - beta^(n) for n ge 1, then value of (a_(10) - 2a_(8))/(2 a_(9)) is :

Let alpha and beta the roots of x^(2) -6x -2=0 with alpha gt beta if alpha_(n) alpha^(n)- beta^(n) for n gt 1 then the value of (a_(10) -2ds)/(2a_(p)) is :

If alpha,beta are the roots of the equation a x^2+b x+c=0, then find the roots of the equation a x^2-b x(x-1)+c(x-1)^2=0 in term of alphaa n dbetadot

If a_(n) = (n^(2))/(2^(n)) , then find a_(7) .

If the ratio of the roots of a_(1)x^(2) + b_(1) x + c_(1) = 0 be equal to the ratio of the roots of a_(2) x^(2) + b_(2)x + c_(2) = 0 , then (a_(1))/(a_(2)) , (b_(1))/(b_(2)) , (c_(1))/(c_(2)) are in :

If a_n =(2n-3)/6 , then find a_(10) ?

HIMALAYA PUBLICATION-QUADRATIC EQUATIONS AND EXPRESSION-Question Bank
  1. Find the condition that quadratic equations x^(2)+ax+b=0 and x^(2)+bx+...

    Text Solution

    |

  2. If both roots of the equation x^(2)-2 a x+a^(2)-1= 0 lie between -2 an...

    Text Solution

    |

  3. If alpha, beta are the roots of a x^(2)+b x+c=0 and A(n)=alpha^(n)+bet...

    Text Solution

    |

  4. If alpha, beta are the roots of x^(2)-a x+b=0 and A(n)='alpha'^(n)+bet...

    Text Solution

    |

  5. In the equation x^(2)+p x+q=0 the coefficient of x was incorrectly wri...

    Text Solution

    |

  6. If sum of the roots of the quadratic equation ax^(2) + bx+c = 0 is equ...

    Text Solution

    |

  7. If a, b, c are in A.P and (b-c) x^(2)+(c-a) x+(a-b)=0 and 2(c+a) x^(2)...

    Text Solution

    |

  8. If A,G and H are respectively A.M.,G.M. and H.M. of three positive num...

    Text Solution

    |

  9. If the ratio of the roots of the equation a x^(2)+b x+c=0 is equal to ...

    Text Solution

    |

  10. If a, b, c are in H . P, then the equation a(b-c) x^(2)+b(c-a) x+c...

    Text Solution

    |

  11. The quadratic equation whose roots are A.M and H . M between the roots...

    Text Solution

    |

  12. Root(s) of the equation 9 x^(2)-18|x|+5=0 belonging to the domain of ...

    Text Solution

    |

  13. Real roots of the equation x^(2)+6|x|+5=0 are

    Text Solution

    |

  14. The sum of the roots of the equation|x^(2)+4 x+3|+2 x+5=0 is

    Text Solution

    |

  15. The set of all real numbers x for which x^(2)-|x+2|+x>0 is

    Text Solution

    |

  16. The sum of the real roots of the equation x^(2)+|x|-12=0 is

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. The sum of distinct values of x such that |x^(2)-x-6|=x+2 is

    Text Solution

    |

  20. Range of the function f(x)=(x^(2)+x+2)/(x^(2)+x+1),x inR is :

    Text Solution

    |