(D) Since $(x-2)$ is a common factor of the expressions $x^2+ax+b$ and $x^2+cx+d$,the value of these expressions at $x=2$ must be $0$.For $x^2+ax+b$:

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(D) Since $(x-2)$ is a common factor of the expressions $x^2+ax+b$ and $x^2+cx+d$,the value of these expressions at $x=2$ must be $0$.For $x^2+ax+b$: $(2)^2+a(2)+b=0 \Rightarrow 4+2a+b=0 \dots(i)$For $x^2+cx+d$: $(2)^2+c(2)+d=0 \Rightarrow 4+2c+d=0 \dots(ii)$Subtracting equation $(ii)$ from equation $(i)$:$(4+2a+b) - (4+2c+d) = 0 - 0$$2a+b-2c-d = 0$$b-d = 2c-2a$$b-d = 2(c-a)$Dividing both sides by $(c-a)$ (assuming $c \neq a$):$\frac{b-d}{c-a} = 2$

Class 11 Mathematics 2 Complex Numbers and Quadratic Equations: Quadratic Equations Solution of quadratic equations and Nature of roots

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If $(x-2)$ is a common factor of the expressions $x^2+ax+b$ and $x^2+cx+d$,then $\frac{b-d}{c-a}$ is equal to

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2 Complex Numbers and Quadratic Equations: Quadratic Equations

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Solution of quadratic equations and Nature of roots

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If $(x-2)$ is a common factor of the expressions $x^2+ax+b$ and $x^2+cx+d$,then $\frac{b-d}{c-a}$ is equal to

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