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Question

A quadratic equation with real coefficients whose one root is $$3-2 i$$ is


A
x23x+2=0
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B
x26x+13=0
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C
x22x+3=0
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D
None of these
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Solution

The correct option is A $$x^2 - 6x + 13 = 0$$
Complex roots occur in conjugate form.
Hence,
Conjugate of $$3-2i$$ will be $$3+2i$$.
Thus, the roots are $$3-2i$$ and $$3+2i$$.
Sum of the roots, is $$6$$.
And product of the roots is $$(3-2i)(3+2i)$$ $$=9+4$$$$=13$$.
Hence, the equation will be 
$$x^{2}-6x+13=0$$.

Mathematics

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