If the equations and

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

If the equations

x^2-3x+4=0

and

4x^2-2[3a+b]x+b=0

, where

a,b\in\mathbb{R}

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

a

is: Note:

[k]

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]