Home
Class 11
MATHS
If f(x) = 27x^3 + 1/x^3 and alpha, beta ...

If `f(x) = 27x^3 + 1/x^3` and `alpha, beta` are the roots of `3x + 1/x = 2` then

A

`f(alpha) = f(beta)`

B

`f(alpha) = 10`

C

`f(beta) = 12`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES

    PATHFINDER|Exercise QUESTION BANK|81 Videos
  • FUNCTIONS

    PATHFINDER|Exercise QUESTION BANK|66 Videos

Similar Questions

Explore conceptually related problems

If f(x)=a+b x+c x^2 and alpha,beta,gamma are the roots of the equation x^3=1,t h e n \ |[a,b,c],[b,c,a],[c,a,b]| is equal to

Let P (x)=x ^(6) -x ^(5) -x ^(3) -x ^(2) -x and alpha, beta, gamma, delta are the roots of the equation x ^(4) -x ^(3)-x ^(2) -1=0, then P (alpha ) + P (beta) +P (gamma) + P(delta)=

If alpha, beta and gamma are the roots of x^3 - x^2-1 = 0, then value of (1+ alpha)/(1-alpha) + (1+ beta) / (1 - beta) + (1 + gamma) / (1 - gamma) is

If alpha and beta be the roots of equation x^(2) + 3x + 1 = 0 then the value of ((alpha)/(1 + beta))^(2) + ((beta)/(1 + alpha))^(2) is equal to

If alpha,beta,gamma are the roots of the equation x^3+p x^2+q x+r=0, then find he value of (alpha-1/(betagamma))(beta-1/(gammaalpha))(gamma-1/(alphabeta)) .

If alpha,beta are the roots of the equation a x^2+b x+c=0, then find the roots of the equation a x^2-b x(x-1)+c(x-1)^2=0 in term of alpha and betadot

IF alpha,beta be the roots of the equation x^2+px+q=0 , show that 1/(alpha+beta) and 1/alpha+1/beta are the roots of pqx^2+(p^2+q)x+p=0

If alpha,beta are the roots of lthe equation 2x ^2-3x-6=0, find the equation whose roots are alpha^2+2 and beta^2+2.

If alpha,beta(alpha < beta) are the roots of equation 6x^2+11x+3="0 , then which following real? (a) cos^(-1)alpha (b) sin^(-1)beta (c) cosec^(-1)alpha (d) both cot^(-1)alpha and cot^(-1)beta

If alpha,beta are the roots of the equation x^2-2x+3=0 obtain the equation whose roots are alpha^3-3alpha^2+5alpha-2 and beta^3-beta^2+beta=5

PATHFINDER-FUNCTION-QUESTION BANK
  1. The value of a for which the range of the function f(x) = (x - 1)/(1 -...

    Text Solution

    |

  2. If the graph of the function f(x) is symmetrical about two lines x = a...

    Text Solution

    |

  3. If f(x) = 27x^3 + 1/x^3 and alpha, beta are the roots of 3x + 1/x = 2 ...

    Text Solution

    |

  4. If A= {x:pi/6 le x le pi/3} and f(x) = cosx - x(1 + x) then f(A) is eq...

    Text Solution

    |

  5. Find the domain of the function f(x) = cos^(-1)(1 + x^2)/(2x) + sqrt...

    Text Solution

    |

  6. Consider the following relations R = {(x,y) |x, y are real number and ...

    Text Solution

    |

  7. Let W denotes the words in the English dictionary Define the relation ...

    Text Solution

    |

  8. If f(x) = sin x + cos x, g (x) = x^2 - 1 then g(f(x)) is invertible in...

    Text Solution

    |

  9. The domain of the functionf(x) = 1/(|x| - x)

    Text Solution

    |

  10. If a function satisfies (x-y) f(x+y)-(x+y) f(x-y) = 2(x^2y - y^3), AA ...

    Text Solution

    |

  11. If f(x) = ax + b and g(x) = cx + d, then f(g(x))=g(f(x)) implies

    Text Solution

    |

  12. Which of the following functions is not injective ?

    Text Solution

    |

  13. If f(x) is defined on [0, 1) by f(x) = { (x, "if x is rational ), (1 -...

    Text Solution

    |

  14. The function f(x) = [x] + sin x ([x] denotes greatest integer le x)

    Text Solution

    |

  15. Let f : R rarr R be defined by f(x) = [x] and g(x) = (3- 2x)/4 then

    Text Solution

    |

  16. If f(x) = 1/ sqrt([cosx]-[sin x])((x) denotes greatest integer le x)) ...

    Text Solution

    |

  17. The graph of the equation y + |y| - x - |x| = 0 is represented by

    Text Solution

    |

  18. If f : R rarr R, defined as f(x) = sin([x]pi)/(x^2 + xz + 1), where [x...

    Text Solution

    |

  19. Let g(x) be a function defined on [-1, 1] so that the area of the equi...

    Text Solution

    |

  20. Let f(x) = x/(1 + x^2) and g(x) = e^(-x)/(1+[x]), where [x] is the gre...

    Text Solution

    |