Question

If equations $a{x}^2+bx+c=0,(a,b,c\in R,a\ne 0)$ and $2x^2+3x+4=0$ have a common root, then $a:b:c$ equals :

• A. $1:2:3$
• B. $2:3:4$
• C. $4:3:2$
• D. $3:2:1$

Answer 1

The correct option is B $2:3:4$

Consider the equation :
$2x^2+3x+4=0$

$\Delta =3^2-4\times 4\times 2=9-32=-23<0$

Hence, the roots are non-real. They will exist in complex conjugate pairs.

As one of the roots is common to $a{x}^2+bx+c=0$ , the other root will also be the complex conjugate of it.

Hence, the roots of the two equations will be the same.

Hence, $a{x}^2+bx+c=k(2x^2+3x+4)$

Hence,
$a:b:c=2:3:4$.