Home
Class 12
MATHS
If f(x) and g(x) are two polynomials suc...

If `f(x)` and `g(x)` are two polynomials such that the polynomial `h(x)=xf(x^3)+x^2g(x^6)` is divisible by `x^2+x+1,` then `f(1)=g(1)` (b) `f(1)=1g(1)` `h(1)=0` (d) all of these

A

`f(1) = g(1)`

B

`f(1) = -g(1)`

C

`f(1) = g(1) ne 0`

D

`f(1) = -g (1) ne 0`

Text Solution

Verified by Experts

The correct Answer is:
A, B
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBER

    FIITJEE|Exercise COMPREHENSION - I|3 Videos

  • COMPLEX NUMBER

    FIITJEE|Exercise COMPREHENSION - II|3 Videos

  • COMPLEX NUMBER

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) Level - I|50 Videos

  • CIRCLE

    FIITJEE|Exercise Numerical Based|2 Videos

  • DEFINITE INTEGRAL

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

Similar Questions

Explore conceptually related problems

If f(x) and g(x) are two polynomials such that the polynomial h(x)=xf(x^(3))+x^(2)g(x^(6)) is divisible by x^(2)+x+1, then ( a )f(1)=g(1) (b) f(1)=1g(1)( ) h(1)=0 (d) all of these

If f(x) and g(x) are two polynomials such that the polynomial P(x)=f(x^(3))+g(x^(3)) is divisible by x^(2)+x+1 , then P(1) is equal to ........

Let g(x) and h(x) are two polynomials such that the polynomial P(x) =g(x^(3))+xh(x^(3)) is divisible by x^(2)+x+1 , then which one of the following is not true?

Let f(x) and g(x) be polynomials with real coefficients.If F(x)=f(x^(3))+xg(x^(3)) is divisible by x^(2)+x+1, then both f(x) and g(x) are divisible by

If the polynomial f(x)=ax^(3)+bx-c is divisible by the polynomial g(x)=x^(2)+bx+c, then ab=( a) 1 (b) (1)/(c) (c) -1(d)-(1)/(c)

If f(x) and g(x) are two polynomials with integers coefficient which vanish at x = 1 / 2, then what is the factor of HCF of f(x) and g(x) ?

If f(x) g(x) and h(x) are three polynomials of degree 2 and Delta = |( f(x), g(x), h(x)), (f'(x), g'(x), h'(x)), (f''(x), g''(x), h''(x))| then Delta(x) is a polynomial of degree (dashes denote the differentiation).

If f(x) and g(x) are two differentiable functions on R^+ such that xf'(x)+g(x)=0 and xg'(x)+f(x)=0 for all x in R^+and f(1)+g(1)=4, then the value of f"(2).g"(2) is

If f(x), g(x), h(x) are polynomials of three degree, then phi(x)=|(f'(x),g'(x),h'(x)), (f''(x),g''(x),h''(x)), (f'''(x),g'''(x),h'''(x))| is a polynomial of degree (where f^n (x) represents nth derivative of f(x))

FIITJEE-COMPLEX NUMBER-ASSIGNMENT PROBLEMS (OBJECTIVE) Level - II
  1. If z=-2 + 2 sqrt3i then z^(2n) + z^(n) + 2^(4n) may be equal to

    Text Solution

    |

  2. The complex number satisfying |z+bar(z)|+|z - bar(z)|=2 and |z+i|+|z-i...

    Text Solution

    |

  3. If |(z1 z- z2)/(z1 z+z2)|=k, (z1 , z2 ne 0) then

    Text Solution

    |

  4. If z1 + a1 + ib1 and z2 = a2 + ib2 are complex such that |z1| = 1, |z2...

    Text Solution

    |

  5. If from a point P representing the complex number z1 on the curve |z...

    Text Solution

    |

  6. If |z1 + z2|=|z1| + |z2|, then one of the value of arguments of the co...

    Text Solution

    |

  7. If the complex numbers z1, z2, z3, z4 taken in that order, represent t...

    Text Solution

    |

  8. One vertex of the triangle of maximum area that can be inscribed in th...

    Text Solution

    |

  9. If x, y, a, b are real numbers such that (x+iy)^(1//5)=a + ib and p = ...

    Text Solution

    |

  10. Let z1, z2 be two complex numbers represented by points on the circle...

    Text Solution

    |

  11. If f(x) and g(x) are two polynomials such that the polynomial h(x)=xf(...

    Text Solution

    |

  12. The complex numbers satisfying |z+2|+|z-2|=8 and |z+6|+|z-6|=12

    Text Solution

    |

  13. If Z= (1+ xi)^(n) be a complex number such that its real and imaginary...

    Text Solution

    |

  14. If z(1),z(2),z(3),…,z(n-1) are the roots of the equation z^(n-1)+z^(n-...

    Text Solution

    |

  15. If ((1+i) z= (1-i))bar(z), then

    Text Solution

    |

  16. Let two distinct complex numbers z1 and z2 both satisfy the equation ...

    Text Solution

    |

  17. If z1 + z2 + z3 = A, z1 + z(2)omega+ z(3)omega^(2)= B, z1 + z(2) omeg...

    Text Solution

    |

  18. A, B, C are the points representing the complex numbers z1, z2, z3 res...

    Text Solution

    |

  19. If 1, omega, omega^2 ,…..,omega^(n-1) are the nth roots of unity, then...

    Text Solution

    |

  20. If omega ne 1 is a cube root of unity , then find the value of |{:(...

    Text Solution

    |