First slide

Theory of equations

Question

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

Moderate

A

$(- 4, 7)$
B

$(4, - 7)$
C

$(4, 7)$
D

$(- 4, - 7)$

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 $(p, q) = (- 4, 7)$ .

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