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anonymous
 one year ago
A quadratic equation with real coefficients and leading coefficient 1, has x = bi as a root. Write the equation in general form.
anonymous
 one year ago
A quadratic equation with real coefficients and leading coefficient 1, has x = bi as a root. Write the equation in general form.

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mathmate
 one year ago
Best ResponseYou've already chosen the best response.2A polynomial with real coefficients has complex roots in conjugate pairs. Hence if one root is bi, the conjugate root is +bi. The quadratic is then f(x)=a(x+bi)(xbi). If the leading coefficient (coefficient of the term of highest degree, namely x^2) is one, then a=1, giving f(x)=(x+bi)(xbi), Expand the expression and write in general form to complete the solution.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how will i write in in general form? :)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2See: https://www.mathsisfun.com/algebra/polynomialsgeneralform.html

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[x ^{2}bi^2 =0 ???

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Almost! But do not forget \(ab^2\) does not equal \((ab)^2=a^2b^2\), and that \(i^2=1\) \(x ^{2}(bi)^2 =0\) Expand the second term and simplify to get the general form.
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