Question

If one root of the equations $x^2+2x+3k=0$ and $2x^2+3x+5k=0$ is common then the value of $k$ is:

• A. $0,1$
• B. $-1,1$
• C. $0,-1$
• D. $2,1$

Answer 1

The correct option is C $0,-1$

Given equation are :

$x^2+2x+3k=0$ ...(1)

$2x^2+3x+5k=0$ ...(2)

Let c be the common root of both the equations, then

at $x=c$, eq. (1) becomes

$c^2+2c+3k=0$

multiplying both sides by $5$,

$5c^2+10c+15k=0$ ...(3)

at $x=c$, eq. $2$ becomes

$2c^2+3c+5k=0$

multiplying both sides by $3$,

$6c^2+9c+15k=0$ ....(4)

adding eq. (3) and (4), we get

$-c^2+c=0$

$c(1-c)=0$

$c=0$ and $c=1$

Now, put $c$ in any eq. (3) or (4), we get

$k=0$ and $k=-1$