Home
Class 11
MATHS
If f(x),g(x) and h(x) are three polynomi...

If `f(x),g(x)` and `h(x)` are three polynomials of degree 2, then prove that `phi(x)` =`|[f(x),g(x),h(x)],[f ^ (prime)(x),g^(prime)(x),h^(prime)(x)],[f^(primeprime)(x),g^(primeprime)(x),h^(primeprime)(x)]|` is a constant polynomial.

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

  • LINEAR INEQUALITIES

    CENGAGE ENGLISH|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

If f(x),g(x)a n dh(x) are three polynomials of degree 2, then prove that varphi(x)=|f(x)g(x)h(x)f^(prime)(x)g^(prime)(x)h^(prime)(x)f^(x)g^(x)h^(x)|i sacon s t a n tpol y nom i a l

If f(x),g(x)a n dh(x) are three polynomials of degree 2, then prove that varphi(x)=|f(x)g(x)h(x)f^(prime)(x)g^(prime)(x)h^(prime)(x)f^(x)g^(x)h^(x)|i sacon s t a n tpol y nom i a l

If f(x),g(x)a n dh(x) are three polynomial of degree 2, then prove that phi(x)=|f(x)g(x)h(x)f'(x)g'(x h '(x)f' '(x)g' '(x )h ' '(x)| is:

If f(x),g(x)a n dh(x) are three polynomial of degree 2, then prove that "phi(x)=|{:(f(x),g(x),h(x)),(f'(x),g'(x),h'(x)),(f''(x),g''(x),h''(x)):}| is a constant polynomial.

If f(x)=x|x|, then prove that f^(prime)(x)=2|x|

If f(x)=x|x|, then prove that f^(prime)(x)=2|x|

If f(x)=x|x|, then prove that f^(prime)(x)=2|x|

If y=|f(x)g(x)h(x)l m n a b c| , prove that (dy)/(dx)=|f^(prime)(x)g^(prime)(x)h^(prime)(x)l m n a b c| .

If f(x) and g(x) are polynomial functions of x, then domain of (f(x))/(g(x)) is

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).

CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. If f(x)=|x+a^2a b a c a b x+b^2b c a c b c x+c^2|,t h e n prove that ...

    Text Solution

    |

  2. If y=cos^(-1)((2x)/(1+x^2)),t h e n(dy)/(dx)i s (a)(-2)/(1+x^2) fo...

    Text Solution

    |

  3. If f(x),g(x) and h(x) are three polynomials of degree 2, then prove th...

    Text Solution

    |

  4. If f(x-y), f(x) f(y) and f(x+y) are in A.P. for all x , y ,and f(0)!=0...

    Text Solution

    |

  5. If x^3+y^3+3a x y=0 , f i n d dy / dx

    Text Solution

    |

  6. If 1 is the twice repeated root of the equation a x^3+b x^2+b x+d=0,t ...

    Text Solution

    |

  7. If log(x^2+y^2)=2tan^(-1)(y/x), show that (dy)/(dx)=(x+y)/(x-y)

    Text Solution

    |

  8. If y=btan^(-1)(x/a+tan^(-1)y/x),find(dy)/(dx)dot

    Text Solution

    |

  9. Let y=sqrt(x+sqrt(x+sqrt(x+oo))) , (dy)/(dx) is equal to (a)1/(2y-1)...

    Text Solution

    |

  10. If y=sqrt(sinx+y), then find (dy)/(dx)

    Text Solution

    |

  11. f(x)=|x^2-3|x|+2|dot Then which of the following is/are true f^(prime)...

    Text Solution

    |

  12. If xsqrt(1+y)+ysqrt(1+x)=0, prove that (dy)/(dx)=-1/((x+1)^2)

    Text Solution

    |

  13. If x^3-2x^2y^2+5x+y-5=0 and y(1)=1, then (a)y^(prime)(1)=4/3 (b) y...

    Text Solution

    |

  14. If x^y=e^(x-y), Prove that (dy)/(dx)=(logx)/((1+logx)^2)

    Text Solution

    |

  15. Let f(x)=(sqrt(x-2sqrt(x-1)))/(sqrt(x-1)-1)xdot Then (a)f^(prime)(10...

    Text Solution

    |

  16. If sqrt(x) +sqrt(y)=4, f i n d (dx/dy) a t (y = 1).

    Text Solution

    |

  17. If y=(x^4-x^2+1)/(x^2+sqrt(3)x+1) and (dy)/(dx)=a x+b , then the value...

    Text Solution

    |

  18. If x y+y^2=tanx+y ,then find (dy)/(dx)

    Text Solution

    |

  19. Which of the following is/are true? (dy)/(dx)fory=sin^(-1)(cosx),w h e...

    Text Solution

    |

  20. If y=sqrt(x+sqrt(y+sqrt(x+sqrt(y+oo)))),t h e np rov et h a t(dy)/(dx)...

    Text Solution

    |