If c and d are the roots of x^2+ax+b=0,then a | vedclass

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(D) Given that $c$ and $d$ are the roots of $x^2+ax+b=0$. From the relation between roots and coefficients,we have $c+d = -a$ and $cd = b$. Now,consid

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$d-2c$

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(D) Given that $c$ and $d$ are the roots of $x^2+ax+b=0$. From the relation between roots and coefficients,we have $c+d = -a$ and $cd = b$. Now,consider the equation $x^2+(4c+a)x+(b+2ac+4c^2)=0$. Substitute $a = -(c+d)$ and $b = cd$ into the equation: $x^2+(4c-(c+d))x+(cd+2c(-(c+d))+4c^2)=0$ $x^2+(3c-d)x+(cd-2c^2-2cd+4c^2)=0$ $x^2+(3c-d)x+(2c^2-cd)=0$ $x^2+(3c-d)x+c(2c-d)=0$ We can factor this as $(x+c)(x+2c-d)=0$. Thus,the roots are $x = -c$ and $x = d-2c$. Comparing with the given options,$d-2c$ is a root.

If $c$ and $d$ are the roots of $x^2+ax+b=0$,then a root of $x^2+(4c+a)x+(b+2ac+4c^2)=0$ is

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