If the equations ax^2 + bx + c = 0 (a, b, c i | vedclass

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(B) Let the common root be $\alpha$. Since $\alpha$ is a root of $2x^2 + 3x + 4 = 0$,it must satisfy the equation.However,the discriminant of $2x^2 +

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$2 : 3 : 4$

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(B) Let the common root be $\alpha$. Since $\alpha$ is a root of $2x^2 + 3x + 4 = 0$,it must satisfy the equation.However,the discriminant of $2x^2 + 3x + 4 = 0$ is $D = 3^2 - 4(2)(4) = 9 - 32 = -23 Since the coefficients are real,the roots must be complex conjugates. Let the roots be $\alpha$ and $\bar{\alpha}$.If the equations $ax^2 + bx + c = 0$ and $2x^2 + 3x + 4 = 0$ have a common root,and the coefficients $a, b, c$ are real,then both roots must be common.Thus,the equations are proportional: $\frac{a}{2} = \frac{b}{3} = \frac{c}{4} = k$ (where $k 
e 0$).Therefore,$a = 2k$,$b = 3k$,and $c = 4k$.This gives the ratio $a : b : c = 2k : 3k : 4k = 2 : 3 : 4$.

If the 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

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