If one of the roots of x^2 + f(a) x + a = 0 is equal to the third power of the other for all real a then

JEE Advanced Mathematics question

If one of the roots of is equal to the third power of the other for all real then

(A)the domain of the real-valued function is the set of non-negative real numbersCorrect
(B)Correct
(C)Correct
(D)none of these

Answer: (A),(B),(C)

Let the roots be and . Then

α+α^3=-f(a), α·α^3=α^4=a.

*Domain.* Since is real-valued, the coefficients are real. If is real then . If is non-real, the roots must be conjugates, , which forces and

Create a free account to read the complete working (6 steps), and practise questions like this in a timed test.

Question ID VK-109189