The quadratic equation with real coefficients | vedclass

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Question

(A) For a quadratic equation with real coefficients,complex roots always occur in conjugate pairs.Given one root is $\alpha = 7 + 5i$,the other root m

Vedclass · Accepted Answer

$x^2 - 14x + 74 = 0$

Vedclass · Answer

(A) For a quadratic equation with real coefficients,complex roots always occur in conjugate pairs.Given one root is $\alpha = 7 + 5i$,the other root must be its conjugate $\beta = 7 - 5i$.The quadratic equation is given by the formula: $x^2 - (\alpha + \beta)x + (\alpha \beta) = 0$.First,calculate the sum of the roots: $\alpha + \beta = (7 + 5i) + (7 - 5i) = 14$.Next,calculate the product of the roots: $\alpha \beta = (7 + 5i)(7 - 5i) = 7^2 - (5i)^2 = 49 - 25i^2 = 49 + 25 = 74$.Substituting these values into the formula,we get: $x^2 - 14x + 74 = 0$.

The quadratic equation with real coefficients whose one root is $7 + 5i$,will be

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