If and , where , have a common root, then the complete set of values of is: Here,…

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

x^2-3x+4=0

and

4x^2-2\lfloor3a+b\rfloor x+b=0

, where

a,b\in\mathbb{R}

, have a common root, then the complete set of values of

a

is: Here,

\lfloor k\rfloor

denotes the greatest integer less than or equal to

k

. (a)

\left[-\frac{11}{3},-\frac{10}{3}\right)

(b)

\left[-\frac{10}{3},-3\right)

(c)

\left[-\frac{10}{3},-3\right]

(d)

\left(3,\frac{10}{3}\right]