Question

If the sum of the cubes of roots of ²+ − = 0 − 6, then b is :

Answer 1

MATHS

If λϵR is such that the sum of the cubes of the roots of the equation, x

2

+(2−λ)x+(10−λ)=0 is minimum, then the magnitude of the difference of the roots of this equation is

ANSWER

By quadratic formula, the roots of this equation are:

α,β=

2

λ−2±

4−4λ+λ

2

−40+4λ

=

2

λ−2±

λ

2

−36

.

The magnitude of the difference of the roots is clearly ∣

λ

2

−36

∣

We have, α

3

+β

3

=

4

(λ−2)

3

+

4

3(λ−2)(λ

2

−36)

=

4

(λ−2)(4λ

2

−4λ−104)

=(λ−2)(λ

2

−λ−26).

This function attains its minimum value at λ=4.

Thus, the magnitude of the difference of the roots is clearly ∣i

20

∣=2

5

.

So the correct answer is option B.