Home
Class 11
MATHS
If alpha,beta are the roots of x^2+p x+q...

If `alpha,beta` are the roots of `x^2+p x+q=0a n dx^(2n)+p^n x^n+q^n=0a n di f(alpha//beta),(beta//alpha)` are the roots of `x^n+1+(x+1)^n=0,t h e nn( in N)` a. must be an odd integer b. may be any integer c. must be an even integer d. cannot say anything

A

an odd integer

B

an even integer

C

any integer

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|50 Videos

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|22 Videos

  • PROBABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|45 Videos

  • SEQUENCES AND SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|59 Videos

Similar Questions

Explore conceptually related problems

Let alpha,beta are the roots of x^2+b x+1=0. Then find the equation whose roots are (alpha+1//beta)a n d(beta+1//alpha) .

If alpha and beta are the roots of x^(2)+4x+6=0 and N=1/((alpha)/(beta)+(beta)/(alpha)) then N=

If alpha,betaa n dgamma are roots of 2x^3+x^2-7=0 , then find the value of sum(alpha/beta+beta/alpha) .

If alpha,beta are the roots of the equation x^2-2x+4=0 , find alpha^(n)+beta^(n) for (a) n=3k, k in N

If alpha,beta are the roots of a x^2+b x+c=0a n dalpha+h ,beta+h are the roots of p x^2+q x+r=0t h e nh= -1/2(a/b-p/q) b. (b/a-q/p) c. 1/2(b/q-q/p) d. none of these

(x+1) is a factor of x^n+1 only if (a)n is an odd integer (b) n is an even integer (c )n is a negative integer (d)n is a positive integer

If alphaa n dbeta are the roots of x^2+p x+q=0a n dalpha^4,beta^4 are the roots of x^2-r x+s=0 , then the equation x^2-4q x+2q^2-r=0 has always. A. one positive and one negative root B . two positive roots C . two negative roots D . cannot say anything

lf alpha and beta are the roots of the equation x^2-ax + b = 0 and A_n = alpha^n + beta^n , then which of the following is true ?

Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic equation x^2-p x+1=0. a n dalpha^2,beta are the roots of quadratic equation x^2-q x+8=0, then find p ,q,alpha,betadot

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

OBJECTIVE RD SHARMA ENGLISH-QUADRATIC EXPRESSIONS AND EQUATIONS -Exercise
  1. If a and b are two distinct real roots of the polynomial f(x) such th...

    Text Solution

    |

  2. If ax^3+ bx - c is divisible by x^2+bx+c, then 'a' is a root of the ...

    Text Solution

    |

  3. If alpha,beta are the roots of x^2+p x+q=0a n dx^(2n)+p^n x^n+q^n=0a n...

    Text Solution

    |

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

    Text Solution

    |

  5. If x=1+i is a root of the equation =x^3-i x+1-i=0, then the other real...

    Text Solution

    |

  6. Let a, b, c be real numbers, a != 0. If alpha is a zero of a^2 x^2+bx...

    Text Solution

    |

  7. If alphaa n dbeta are the roots of x^2+p x+q=0a n dalpha^4,beta^4 are ...

    Text Solution

    |

  8. The equation (cosp-1)^x^2+(cos p)x+s in p=0 in the variable x has real...

    Text Solution

    |

  9. The number of real solution of the equation. sin(e^(x))=5^(x)+5^(-x) ...

    Text Solution

    |

  10. Suppose that f(x) is a quadratic expresson positive for all real xdot ...

    Text Solution

    |

  11. If c ,d are the roots of the equation (x-a)(x-b)-k=0 , prove that a, b...

    Text Solution

    |

  12. Show that A.M. of the roots of x^(2) - 2ax + b^(2) = 0 is equal to ...

    Text Solution

    |

  13. If alpha, beta are the roots of the quadratic equation x ^(2)+ px+q=0...

    Text Solution

    |

  14. If the roots of the equation (1)/(x+p) +(1)/(x+q) =1/r are equal in ma...

    Text Solution

    |

  15. If the ratio of the roots of the equation x^(2)+px+q=0 is equal to the...

    Text Solution

    |

  16. Find the value of p for which x+1 is a factor of x^4+(p-3)x^3-(3p-5)x^...

    Text Solution

    |

  17. If x ^(2) -3x+2 is a factor of x ^(4) -px ^(2) +q=0, then p+q=

    Text Solution

    |

  18. If the equations x^2+p x+q=0 and x^2+p^(prime)x+q^(prime)=0 have a com...

    Text Solution

    |

  19. If the expression x^(2) - 11x + a and x^(2) - 14 x + 2a have a common ...

    Text Solution

    |

  20. If a,b,c are in GP, show that the equations ax^(2)+2bx+c=0 and dx^(2)+...

    Text Solution

    |