Mathematics - Quadratic Equation Question with Solution | TestHub

$a{x}^2+bx+c=0$....(i)

$2x^2+3x+4=0$....(ii)

For equation (ii),$D=9-4\left(2\right)\left(4\right)=-23<0$

Roots are complex conjugates.

$\Rightarrow$Both roots are common in equation (i) and (ii).

$\therefore \frac{\text{a}}{2}=\frac{\text{b}}{3}=\frac{\text{c}}{4}$

$\text{⇒ a}\text{ : }\text{b}\text{ : }\text{c}\text{ : : }2\text{ : }3\text{ : }4$