A) \[{{x}^{2}}+4x+13=0\]
B) \[{{x}^{2}}+4x-13=0\]
C) \[{{x}^{2}}-4x+13=0\]
D) \[{{x}^{2}}-4x-13=0\]
E) \[{{x}^{2}}+2x+13=0\]
Correct Answer: C
Solution :
If one root is\[2+3i,\]then another root will be\[2-3i\]. \[\therefore \] Sum of roots \[=2+3i+2-3i=4\] and product of roots\[=(2+3i)\text{ }(2-3i)\] \[=4+9=13\] \[\therefore \]Required equation is \[{{x}^{2}}-(sum\text{ }of\text{ }roots)x+(product\text{ }of\text{ }roots)=0\] \[{{x}^{2}}-4x+13=0\]
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