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  4. If equations ax2 + bx + c = 0, (a, b, c ∈ R, a ≠ 0) and 2x2 + 3x + 4 = 0 have a common root, then a: b: c equals :

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

JEE MainJEE Main 2014Complex Numbers and Quadratic Equations

Solution:

$2x^{2}+3x+4=0\,$as $D \le0$
$\Rightarrow $ both roots are imaginary
$\Rightarrow $ both roots arecommon
$\Rightarrow \frac{a}{2}=\frac{b}{3}=\frac{c}{4}$