If the equations x^2 + 2x + 3 = 0 and ax^2 + | vedclass

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(A) If two quadratic equations $A_1x^2 + B_1x + C_1 = 0$ and $A_2x^2 + B_2x + C_2 = 0$ have the same roots,then their coefficients are proportional,i.

Vedclass · Accepted Answer

$1 : 2 : 3$

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(A) If two quadratic equations $A_1x^2 + B_1x + C_1 = 0$ and $A_2x^2 + B_2x + C_2 = 0$ have the same roots,then their coefficients are proportional,i.e.,$\frac{A_1}{A_2} = \frac{B_1}{B_2} = \frac{C_1}{C_2} = k$.Given equations are $x^2 + 2x + 3 = 0$ and $ax^2 + bx + c = 0$.Comparing the coefficients,we get $\frac{a}{1} = \frac{b}{2} = \frac{c}{3} = k$.This implies $a = k$,$b = 2k$,and $c = 3k$.Therefore,the ratio $a : b : c = k : 2k : 3k = 1 : 2 : 3$.

If the equations $x^2 + 2x + 3 = 0$ and $ax^2 + bx + c = 0$,where $a, b, c \in R$,have the same roots,then what is the ratio $a : b : c$?

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