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

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(B) Given that the equations $ax^2 + bx + c = 0$ and $2x^2 + 3x + 4 = 0$ have a common root.For two quadratic equations $a_1x^2 + b_1x + c_1 = 0$ and

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$2 : 3 : 4$

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(B) Given that the equations $ax^2 + bx + c = 0$ and $2x^2 + 3x + 4 = 0$ have a common root.For two quadratic equations $a_1x^2 + b_1x + c_1 = 0$ and $a_2x^2 + b_2x + c_2 = 0$ to have a common root,the coefficients must be proportional if both roots are common,or we can use the condition for a single common root.However,in this case,the discriminant of the second equation $2x^2 + 3x + 4 = 0$ is $D = b^2 - 4ac = 3^2 - 4(2)(4) = 9 - 32 = -23$.Since $D Therefore,the two equations must be proportional:$\frac{a}{2} = \frac{b}{3} = \frac{c}{4} = k$This implies $a = 2k$,$b = 3k$,and $c = 4k$.Thus,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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