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

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

Complex Numbers and Quadratic Equations

Solution:

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$\alpha+\beta= c , \alpha \cdot \beta= d , \alpha^2= b , 2 \alpha= a$
Now, $2(b+d)=2\left(\alpha^2+\alpha \beta\right)=2 \alpha(\alpha+\beta)=$ ac.