The equation of smallest degree with real coefficients having 2 + 3i as one of the roots is

Question

The equation of smallest degree with real coefficients having $2 + 3 i$ as one of the roots is

Smart Achievers · Accepted Answer

(3)

$Since complex roots always exist in pairs$

$So other root will be 2 - 3 i$

$S = sum of roots = 2 + 3 i + 2 - 3 i = 4$

$P = Product of roots = (2 + 3 i) (2 - 3 i) = 4 + 9 = 13$

$So, required equation will be$

$x^{2} - S x + P = 0$ $\Rightarrow x^{2} - 4 x + 13 = 0$

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