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

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise All Questions|365 Videos

  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 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

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. The region of argand diagram defined by |z-1|+|z+1|<=4 (1) interior o...

    Text Solution

    |

  2. z1, z2, z3,z4 are distinct complex numbers representing the vertices o...

    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. If (log)(sqrt(3))((|z|^2-|z|+1)/(2+|z|))>2, then locate the region in ...

    Text Solution

    |

  5. If z=((1+isqrt3)^2)/(4i(1-isqrt3)) is a complex number then a. arg(...

    Text Solution

    |

  6. If alpha,beta,gamma are such that alpha+beta+gamma=2,""alpha^2+beta^2+...

    Text Solution

    |

  7. If z=3/(2+costheta+"isin"theta) then locus of z is straight line a c...

    Text Solution

    |

  8. If z=x +i y such that |z+1|=|z-1| and arg((z-1)/(z+1))=pi/4 , then fin...

    Text Solution

    |

  9. If x y=2(x+y),xlt=y and x ,y in N , then the number of solutions of t...

    Text Solution

    |

  10. If I m((z-1)/(e^(thetai))+(e^(thetai))/(z-1))=0 , then find the locus ...

    Text Solution

    |

  11. If pa n dq are distinct prime numbers, then the number of distinct im...

    Text Solution

    |

  12. The number of real solutions of the equation (9//10)^x=-3+x-x^2 is a. ...

    Text Solution

    |

  13. What is locus of z if |z-1-sin^(-1)(1/sqrt3)|+|z+cos^(-1)(1/sqrt3)-p...

    Text Solution

    |

  14. If |z-2-i|=|z|sin(pi/4-a r g z)| , where i=sqrt(-1) ,then locus of z,...

    Text Solution

    |

  15. The number of integral values of a for which the quadratic equation (x...

    Text Solution

    |

  16. omega is an imaginary root of unity. Prove that (i) ( a + bomeg...

    Text Solution

    |

  17. If z is a complex number having least absolute value and |z-2+2i|=1,th...

    Text Solution

    |

  18. If the equation cot^4x-2cos e c^2x+a^2=0 has at least one solution, t...

    Text Solution

    |

  19. Which of the following is equal to root(3)(-1) a. (sqrt(3)+sqrt(-1))/...

    Text Solution

    |

  20. omega is an imaginary root of unity. Prove that (a+bomega+comega^2)^3+...

    Text Solution

    |