(B) Let $y$ be a common root of $x^2+5ax+6=0$ and $x^2+3ax+2=0$. Since $y$ satisfies both equations,we have: $y^2+5ay+6=0$ $(1)$ $y^2+3ay+2=0$ $(2)$ S

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(B) Let $y$ be a common root of $x^2+5ax+6=0$ and $x^2+3ax+2=0$. Since $y$ satisfies both equations,we have: $y^2+5ay+6=0$ $(1)$ $y^2+3ay+2=0$ $(2)$ Subtracting equation $(2)$ from $(1)$: $(y^2+5ay+6) - (y^2+3ay+2) = 0$ $2ay + 4 = 0$ $2ay = -4$ $ay = -2$ Substitute $ay = -2$ into equation $(2)$: $y^2 + 3(-2) + 2 = 0$ $y^2 - 6 + 2 = 0$ $y^2 - 4 = 0$ $y^2 = 4$ $y = \pm 2$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Condition for common roots

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If $x^2+5ax+6=0$ and $x^2+3ax+2=0$ have a common root,then that common root is

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$3$ (or) $-3$
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$2$ (or) $-2$
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$2$ (or) $-3$
D
$-2$ (or) $3$

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