Home
Class 12
MATHS
Let f(x)=a(5)x^(5)+a(4)x^(4)+a(3)x^(3)+a...

Let `f(x)=a_(5)x^(5)+a_(4)x^(4)+a_(3)x^(3)+a_(2)x^(2)+a_(1)x, "where" a_(i),s` are real and f (x) = 0 has a positive root `alpha_(0).` Then `f^(prime)(x)=0` has a positive root `alpha_1` such that 0 < `alpha_1` < `alpha_0` `f^(prime)(x)=0` has at least two real roots `f^('')(x)=0` has at least one real root none of these

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

Let (1+x+x^(2))^(9)=a_(0)+a_(1)x+a_(2)x^(2)+.....+a_(18)x^(18) . Then

Let (1+x+x^(2))^(9)=a_(0)+a_(1)x+a_(2)x^(2)+......+a_(18)x^(18) . Then

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 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 -

If (1+2x+x^(2))^(n) = sum_(r=0)^(2n)a_(r)x^(r) , then a_(r) =

If (x^(2)+x+1)/(1-x) = a_(0) + a_(1)x+a_(2)x^(2)+"…." , then sum_(r=1)^(50) a_(r) equal to

Let (x+10)^(50)+(x-10)^(50)=a_(0)+a_(1)x+a_(2)x^(2)+...+a_(50)x^(50) for all x in R , then (a_(2))/(a_(0)) is equal to

If p(x)=a_(0)x^(n)+a_(1)x^(n-1)+a_(2)x^(n-2)+.....+a_(n-1)x+a_(n)," prove that " underset(xrarra)"lim" p(x)=p(a) .

If (1+x) ^(15) =a_(0) +a_(1) x +a_(2) x ^(2) +…+ a_(15) x ^(15), then the value of sum_(r=1) ^(15) r . (a_(r))/(a _(r-1)) is-

If (1+x+x^(2))^(25)=a_(0)+a_(1)x+a_(2)x^(2)+...+a_(50).x^(50) , then a_(0)+a_(2)+a_(4)+....+a_(50) is

If (3x-1)^(7)=a_(7)x^(7)+a_(6)x^(6)+a_(5)x^(5)+.......+a_(1)x+a_(0) , then find the value of a_(7)+a_(6)+a_(5)+...........+a_(0) .

CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. Which of the following is not the root of the equation |[x,-6,-1],[ 2,...

    Text Solution

    |

  2. If A,B,C are the angles of a non right angled triangle ABC. Then find ...

    Text Solution

    |

  3. Let f(x)=a(5)x^(5)+a(4)x^(4)+a(3)x^(3)+a(2)x^(2)+a(1)x, "where" a(i),s...

    Text Solution

    |

  4. Evaluate |(cosalphacosbeta,cosalpha sinbeta , - sin alpha),(-sin beta,...

    Text Solution

    |

  5. Roots of the equation |x m n1a x n1a b x1a b c1|)=0 are independent ...

    Text Solution

    |

  6. Prove that the value of each the following determinants is zero: |[a...

    Text Solution

    |

  7. If a ,b ,c are different, then the value of x satisfying |[0,x^2-a, x^...

    Text Solution

    |

  8. Prove that the value of each the following determinants is zero: |...

    Text Solution

    |

  9. If |(b +c,c +a,a +b),(a +b,b +c,c +a),(c +a,a +b,b +c)| = k |(a,b,c),(...

    Text Solution

    |

  10. A triangle has vertices Ai(xi , yi)fori=1,2,3 If the orthocentre of tr...

    Text Solution

    |

  11. If alpha,beta,gamma are the roots of a x^3+b x^2+cx+d=0 and |[alpha,b...

    Text Solution

    |

  12. If Delta=|(a1,b1,c1),(a2,b2,c2),(a3,b3,c3)| and Delta1=|(a1+pb1,b1+q...

    Text Solution

    |

  13. Prove that the value of each the following determinants is zero: |[(a^...

    Text Solution

    |

  14. The value of the determinant |(1^2, 2^2, 3^2, 4^2) ,(2^2, 3^2 ,4^2,5^2...

    Text Solution

    |

  15. If f(x)= |1 x x+1 2x x(x-1)(x+1)x3x(x-1)x(x-1)(x-2)(x+1)x(x-1)| then f...

    Text Solution

    |

  16. Prove that the value of each the following determinants is zero: |[l...

    Text Solution

    |

  17. If the system of equations x-k y-z=0, k x-y-z=0,x+y-z=0 has a nonzero ...

    Text Solution

    |

  18. Show that |[1,1+p,1+p+q],[2,3+2p,1+3p+2q],[3,6+3p,1+6p+3q]|= 1

    Text Solution

    |

  19. By using properties of determinants. Show that: |1+a^2-b^2; 2ab; -2b: ...

    Text Solution

    |

  20. Which of the following values of alpha satisfying the equation |(1+alp...

    Text Solution

    |