Home
Class 12
MATHS
If the equation a(n) x^(n) + a(n -1) x^(...

If the equation `a_(n) x^(n) + a_(n -1) x^(n-1) + .... + a_(1) x = 0, a_(1) ne 0, n ge 2 `, has a positive root x = `alpha `, then the equation n `a_(n) x^(n-1) + (n - 1) a_(n-1) x^(n-1) + ..... , a_(1) = 0 ` has a positive root, which is :

A

a positive root less than `alpha`

B

a positive root larger than `alpha`

C

a negative root

D

no positive root

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|200 Videos

Similar Questions

Explore conceptually related problems

If n^(th) term of the sequences is a_(n)= (-1)^(n-1)5^(n+1) , Find a_(3) ?

Find the sixth term of the sequence a_(n) =(n)/(n+1) ?

Write the first three terms of the sequence a_(n)=(-1)^(n-1) 5^(n+1)

If 1, a_(1), a_(2). ..., a_(n-1) are n roots of unity, then the value of (1 - a_(1)) (1 - a_(2)) .... (1 - a_(n-1)) is :

If a_(1)=1, a_(2)=5 and a_(n+2)=5a_(n+1)-6a_(n), n ge 1 , show by using mathematical induction that a_(n)=3^(n)-2^(n)

Let ( a_(n) ) be a G.P. such that ( a_(4))/( a_(6)) =( 1)/( 4) and a_(2) + a_(5) = 216 . Then a_(1) =

For a positive integer n, let a_(n) = 1+( 1)/( 2) +( 1)/( 3) + ( 1)/( 4) + "......." + ( 1)/(( 2^(n) - 1)) . Then :

If m and n are the roots of the equations x^(2) - 6x+ 2 =0 then the value of (1)/(m) + (1)/( n) is :

If alpha, beta are the roots of x^(2)-a x+b=0 and A_(n)='alpha'^(n)+beta^(n) , then A_(n+1)=

Let (1+x^(2))^(2)(1+x)^(n) = sum_(k=0)^(n+4) a_(k) x^(k) . If a_(1) , a_(2) , a_(3) are in A.P., then n=

HIMALAYA PUBLICATION-APPLICATION OF DIFFERENTIATION-QUESTION BANK
  1. A stone is thrown vertically upwards from the top of a tower 64 metres...

    Text Solution

    |

  2. The tangent to a given curve y=f(x) is perpendicular to the x -axis if

    Text Solution

    |

  3. A sphere increases its volume at the rate of picc//s. The rate at whic...

    Text Solution

    |

  4. The angle between y^(2)=4x and x^(2)+y^(2)=12 at a point of their inte...

    Text Solution

    |

  5. The slopes of the tangent and normal at (0, 1) for the curve y=sinx+e^...

    Text Solution

    |

  6. If for the curve y=1+bx-x^(2) the tangent at (1, -2) is parallel to x-...

    Text Solution

    |

  7. The surface area of a ball is increasing at the rate of 2 pi sq. cm/s...

    Text Solution

    |

  8. If the area of an expanding circular region increases at a constant ra...

    Text Solution

    |

  9. If f(x)=x^(alpha) logx and f(0)=0, then the value of alpha for which R...

    Text Solution

    |

  10. A point an the parabola y^(2)=18x at which the ordinate increases at t...

    Text Solution

    |

  11. If 2 a+3 b+6 c=0, a, b, c in R then the equation a x^(2)+b x+c=0 has a...

    Text Solution

    |

  12. Let f be differentiable for all x. If f(1)= -2, f'(x) ge 2 for all x ...

    Text Solution

    |

  13. If the equation a(n) x^(n) + a(n -1) x^(n-1) + .... + a(1) x = 0, a(1)...

    Text Solution

    |

  14. If a+b+c=0, then the equation 3ax^(2)+2bx+c=0 has :

    Text Solution

    |

  15. If f(x) satisfiles requirements of Rolle's theorem in [1,2] and f(x) i...

    Text Solution

    |

  16. Let f(x) = e^(x), x in [0,1], then a number c of the Lagrange's mean v...

    Text Solution

    |

  17. If f(x) satisfies of conditions of Rolle's theorem on [3,5], then int3...

    Text Solution

    |

  18. The function f(x) = x(x+3)e^(-x/2) satisfies all the conditions of Rol...

    Text Solution

    |

  19. In a triangle ABC if sides a and b remain constant such that alpha is ...

    Text Solution

    |

  20. The circumference of a circle is measured as 56 cm with an error 0.02 ...

    Text Solution

    |