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

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 (a)`f(1)=g(1)` (b) `f(1)=1g(1)` (c)`h(1)=0` (d) all of these

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP|Exercise All Questions|7 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 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) 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) is polynomial function such that f(x)+f'(x)+f(x)+f'(x)=x^(3) and g(x)=int(f(x))/(x^(3)) and g(1)=1 then g( e ) is

If f(1) =g(1)=2 , then lim_(xrarr1) (f(1)g(x)-f(x)g(1)-f(1)+g(1))/(f(x)-g(x)) is equal to

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).

RESONANCE DPP-JEE MAINS-All Questions
  1. A boy has 3 library tickets and 8 books of his interest in the library...

    Text Solution

    |

  2. Find the values of alpha for which the point (alpha-1,alpha+1) lies in...

    Text Solution

    |

  3. Which of the following correspondences can not be called a function ...

    Text Solution

    |

  4. Determine the matrices A and B where A + 2B = [(1, 2, 0), (6, -3, 3),...

    Text Solution

    |

  5. If the equation x^(5)-10a^(3)x^(2)+b^(4)x+c^(5)=0 has three equal root...

    Text Solution

    |

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

    Text Solution

    |

  7. Let a x+b y+c=0 be a variable straight line, whre a , ba n dc are the ...

    Text Solution

    |

  8. If f(x) be a twice differentiable function from RR rarr RR such that t...

    Text Solution

    |

  9. Let y be an element of the set A={1,2,3,4,5,6,10,15,30} and x(1), x(2)...

    Text Solution

    |

  10. Suppose x, y in (-2, 2) and xy=-1, then the minimum value of a=4/(4-x...

    Text Solution

    |

  11. A chess game between two grandmasters X and Y is won by whoever first ...

    Text Solution

    |

  12. A complex number z with (Im)(z)=4 and a positive integer n be such tha...

    Text Solution

    |

  13. The function f(x)=x^2e^(-2x),x > 0. If l is maximum value of f(x) find...

    Text Solution

    |

  14. Find the sum of sum(r=1)^n(r^n Cr)/(^n C(r-1) .

    Text Solution

    |

  15. The sum of all 3 digit-numbers formed using 1, 2, 3  repetition is ...

    Text Solution

    |

  16. The number of integral points (x,y) (i.e, x and y both are integers) w...

    Text Solution

    |

  17. If the system of linear equations x+2ay +az =0,x+3by+bz =0 and x+4cy ...

    Text Solution

    |

  18. If y=(1+x)(1+x^2)(1+x^4)(1+x^(2n)), then find (dy)/(dx)a tx=0.

    Text Solution

    |

  19. Using truth tables, prove the following equivalences : (1) ~pvvq-=~(...

    Text Solution

    |

  20. The area of the region bounded by the curve y= 2x -x^(2) and x...

    Text Solution

    |