Question

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

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

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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