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  4. If 2+ i √3 is a root of the equation x 2+ px + q =0, where p and q are real, then ( p , q )=

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Q. If $2+ i \sqrt{3}$ is a root of the equation $x ^{2}+ px + q =0$, where $p$ and $q$ are real, then $( p , q )=$

Complex Numbers and Quadratic Equations

Solution:

Since $2+ i \sqrt{3}$ is a root, therefore, $2- i \sqrt{3}$ will be other root. Now sum of the roots $=4=- p$ and product of roots $=7= q .$ Hence $( p , q )=(-4,7)$