The quadratic equation with real coefficients | vedclass

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Question

(A) Since the coefficients are real,the complex roots must occur in conjugate pairs.Given one root is $\alpha = 7 + 5i$,the other root must be $\beta

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) Since the coefficients are real,the complex roots must occur in conjugate pairs.Given one root is $\alpha = 7 + 5i$,the other root must be $\beta = 7 - 5i$.The sum of the roots is $\alpha + \beta = (7 + 5i) + (7 - 5i) = 14$.The product of the roots is $\alpha \beta = (7 + 5i)(7 - 5i) = 7^2 - (5i)^2 = 49 + 25 = 74$.The quadratic equation is given by $x^2 - (	ext{sum of roots})x + (	ext{product of roots}) = 0$.Substituting the values,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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