Home
Class 12
MATHS
Consider biquadratic equation 81x^(4) + ...

Consider biquadratic equation `81x^(4) + 216x^(3) + 96x = 65`, whose roots are `a,b,c,d`. Given `a,b`, real roots and `c,d` are imaginary roots.
On the basis of above information, answer the followin questions:
The Value of `c^(3) + d^(3) - (a+b))^(3)` is equal to

A

`(52)/(9)`

B

`(53)/(9)`

C

`(59)/(9)`

D

`(50)/(9)`

Text Solution

Verified by Experts

The correct Answer is:
A
The given equation is ltbgt `(3x+2)^(4) = 81`
`implies ((3x+2)^(2)-9)((3x+2)^(2)+9)=0`
Let `a=(1)/(3),b=(-5)/(3),C=(-2)/(3)+i,d=(-2)/(3)-i`
Now,verfiy it
Promotional Banner

Topper's Solved these Questions

  • TEST PAPERS

    ALLEN|Exercise part-2 Mathematics|18 Videos

  • TEST PAPERS

    ALLEN|Exercise part-2 Mathematic|18 Videos

  • TEST PAPER

    ALLEN|Exercise CHEMISTRY SECTION-II|8 Videos

  • VECTOR ALGEBRA

    ALLEN|Exercise All Questions|1 Videos

Similar Questions

Explore conceptually related problems

Consider biquadratic equation 81x^(4) + 216x^(3) + 216x^(2) +96x = 65 , whose roots are a,b,c,d . Given a,b , real roots and c,d are imaginary roots. On the basis of above information, answer the followin questions: The value of (a+b)^(3) - (c+d)^(3) is equal to-

The equation (6-x)^4+(8-x)^4=16 has (A) sum of roots 28 (B) product of roots 2688 (C) two real roots (D) two imaginary roots

If a,b,c,d in R, then the equation (x^(2)+ax-3b)(x^(2)-cx+b)(x^(2)-dx+2b)=0 has a.6 real roots b.at least 2 real roots c.4 real roots d.none of these

If the roots of the equation x^(3) + bx^(2) + cx + d = 0 are in arithmetic progression, then b, c and d satisfy the relation

If a

The roots of the equation a^(2)x^(2)+(a+b)x-b^(2)=0(a,b!=0) are :(A) real and different (B) real and equal (C) imaginary (D) None

If c and d are roots of the equation (x-a) (x-b) - k = 0, then a, b are roots of the equation

The value of k for which the quadratic equation kx^(2)+1=kx+3x-11x^(2) has real and equal roots are (a)-11,-3,(b)5,7(c)5,-7(d) none of these