If the two equations x^2 - cx + d = 0 and x^2 | vedclass

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(C) Let the roots of $x^2 - cx + d = 0$ be $\alpha$ and $\beta$.Since the second equation $x^2 - ax + b = 0$ has equal roots and shares one common roo

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$ac$

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(C) Let the roots of $x^2 - cx + d = 0$ be $\alpha$ and $\beta$.Since the second equation $x^2 - ax + b = 0$ has equal roots and shares one common root $\alpha$ with the first,its roots must be $\alpha$ and $\alpha$.From the properties of roots:For the first equation: $\alpha + \beta = c$ and $\alpha \beta = d$.For the second equation: $\alpha + \alpha = a \implies 2\alpha = a$ and $\alpha^2 = b$.We need to find $2(b + d)$.Substituting the values: $2(b + d) = 2(\alpha^2 + \alpha \beta) = 2\alpha(\alpha + \beta)$.Since $2\alpha = a$ and $\alpha + \beta = c$,we get $2(b + d) = a 	imes c = ac$.

If the two equations $x^2 - cx + d = 0$ and $x^2 - ax + b = 0$ have one common root and the second equation has equal roots,then $2(b + d) = $

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