Question

If $x=2$ and $x=3$ are roots of the equation $3x^2-2kx+2m=0$ then $(k,m)$=

• A. $(\frac{15}{2},9)$
• B. $(9,\frac{15}{2})$
• C. $(\frac{9}{2},15)$
• D. ( 15 , 8)

Answer 1

The correct option is A $(\frac{15}{2},9)$

Since $x=2$ and $x=3$ are roots of the equation $3x^2-2kx+2m=0$
$\Rightarrow 12-4k+2m=0\Rightarrow 2k-m=6$ ...(i)
and $\Rightarrow 27-6k+2m=0\Rightarrow 6k-2m=27$ ...(ii)
On multiplying (i) by 3 and subtracting (ii) from it, we get
$6k-3m=18$
$\underset{–}{\underset{-}{6}k\underset{+}{-}2m=\underset{-}{2}7}$
$-m=-9$
$\therefore m=9$
On putting $m=9$ in (i), we get
$2k=15\Rightarrow k=\frac{15}{2}$
$\therefore (k,m)=(\frac{15}{2},9)$
Hence, Option A is correct.