Home
Class 11
MATHS
If the polynomial equation an x^n + a(n-...

If the polynomial equation `a_n x^n + a_(n-1) x^(n-1) + a_(n-2) x^(n-2) + ....... + a_0 = 0, n` being a positive integer, has two different real roots `a` and `b`. then between `a` and `b` the equation `na_n x^(n-1) +(n-1)a_(n-1) x^(n-2) +.......+a_1 =0` has

A

exactly one root

B

almost one root

C

at least one root

D

no root

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • MEAN VALUE THEOREMS

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|4 Videos

  • MATRICES

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos

  • PAIR OF STRAIGHT LINES

    OBJECTIVE RD SHARMA|Exercise Chapter Test|19 Videos

Similar Questions

Explore conceptually related problems

If the equation a_(n)x^(n)+a_(n-1)x^(n-1)+..+a_(1)x=0, a_(1)!=0, n ge2 , has a positive root x=alpha then the equation na_(n)x^(n-1)+(n-1)a_(n-1)x^(n-2)+….+a_(1)=0 has a positive root which is

Differentiate |x|+a_(0)x^(n)+a_(1)x^(n-1)+a_(2)x^(n-1)+...+a_(n-1)x+a_(n)

(1+x)^(n)=a_(0)+a_(1)x+a_(2)*x^(2)+......+a_(n)x^(n) then prove that

Evaluate lim_(xrarrc) f(x) where f(x) = a_nx^n+a_(n-1)x^(n-1)+a_(n-2)x^(n-2)+.....+a_2x^2+a_1x^1+a_0

Let a_(0)/(n+1) +a_(1)/n + a_(2)/(n-1) + ….. +(a_(n)-1)/2 +a_(n)=0 . Show that there exists at least one real x between 0 and 1 such that a_(0)x^(n) + a_(1)x^(n-1) + …..+ a_(n)=0

Prove that if the equation a_(0)x^(n)+a_(1)x^(n-1)+….+ a_(n-1) x = 0 has a positive root x_(0) , then the equation na_(0)x^(n-1) +(n-1) a_(1)x^(n-2) +….+ a_(n-1) =0 has a positive root less than x_(0) .

Let f(x) = a_(0)x^(n) + a_(1)x^(n-1) + a_(2) x^(n-2) + …. + a_(n-1)x + a_(n) , where a_(0), a_(1), a_(2),...., a_(n) are real numbers. If f(x) is divided by (ax - b), then the remainder is

If the sequence {a_n}, satisfies the recurrence, a_(n+1) = 3a_n - 2a_(n-1), n ge2, a_0 = 2, a_1 = 3, then a_2007 is

If the equation a_0x^n +a_1x^(n-1) +....a_(n-1)x=0 has a positive root alpha prove that the equation na_0x^(n-1) +(n-1)a_1 x^(n-2) + ---+a_(n-1) = 0 also has a positive root smaller than alpha

Differentiate the following with respect of x:a_(0)x^(n)+a_(1)x^(n-1)+a_(2)x^(n-2)++a_(n-1)x+a_(n)

OBJECTIVE RD SHARMA-MEAN VALUE THEOREMS-Exercise
  1. Let fa n dg be differentiable on [0,1] such that f(0)=2,g(0),f(1)=6a n...

    Text Solution

    |

  2. If the polynomial equation an x^n + a(n-1) x^(n-1) + a(n-2) x^(n-2) + ...

    Text Solution

    |

  3. The equation x log x = 3-x has, in the interval (1,3) :

    Text Solution

    |

  4. If f(x) and g(x) ar edifferentiable function for 0lex le1 such that f(...

    Text Solution

    |

  5. If alpha beta( alpha lt beta) are two distinct roots of the equation. ...

    Text Solution

    |

  6. If (x) is a function given by f(x) = |{:(sinx , sin a, sin b),(cosx,c...

    Text Solution

    |

  7. The value of c in Largrange's theorem for the function f(x)= log(e) s...

    Text Solution

    |

  8. n is a positive integer. If the value of c presecribed in Rolle's th...

    Text Solution

    |

  9. The distance travelled by a particle upto tiem x is given by f(x)=x^(...

    Text Solution

    |

  10. The number of real root of the equation e^(x-1)+x-2=0, is

    Text Solution

    |

  11. If the polynomial equation an x^n + a(n-1) x^(n-1) + a(n-2) x^(n-2) + ...

    Text Solution

    |

  12. If 4a+2b+c=0 , then the equation 3ax^(2)+2bx+c=0 has at least one rea...

    Text Solution

    |

  13. For the function f(x) = x + 1/x, x in [1,3] , the value of c for me...

    Text Solution

    |

  14. If from Largrange's mean value theorem, we have f(x'(1))=(f'(b)-f(a))...

    Text Solution

    |

  15. Rolle's theorem is applicable in case of phi(x) = a^sin x,a>0 in

    Text Solution

    |

  16. The value of c in Rolle's theorem when f(x)=2x^(3)-5x^(2)-4x+3, x in [...

    Text Solution

    |

  17. When the tangent the curve y=x log (x) is parallel to the chord joinin...

    Text Solution

    |

  18. The value of c in Rolle's theorem for the function f (x) =(x(x+1))/e^x...

    Text Solution

    |

  19. The value of c in Largrange's mean value theorem for the function f(...

    Text Solution

    |

  20. The value of c in Rolle's theorem for the function f(x) = x^(3) - 3...

    Text Solution

    |