First slide

Theory of equations

Question

If the equations $a x^{2} + b x + c = 0$ and $2 x^{2} + 3 x + 4 = 0$ a common root, then $a : b : c$

Moderate

A

2 : 3 : 4
B

1 : 2 : 3
C

4 : 3 : 2
D

none of these

Solution

The equation $2 x^{2} + 3 x + 4 = 0$ has complex roots
which always occur in pairs. So, the two equations have both roots common.
$∴ \frac{a}{2} = \frac{b}{3} = \frac{c}{4} \Rightarrow a : b : c = 2 : 3 : 4$

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