Answers

2014-09-18T22:31:02+08:00
An odd number is an integer which is not a multiple of two .

odd \ numbers \ are: \ 1, \ 3, \ 5, \ 7, \ 9 , \ 11, \ 13, \ 15, \ 17, ....


x^2-4x+12 =0 \\a=1, \ \ b=-4 , \ \ c=12 \\ \\ x_{1}=\frac{-b-\sqrt{b^2-4ac}}{2a}=\frac{4-\sqrt{ (-4)^2-4 \cdot1 \cdot12 }}{2 }= \frac{4-\sqrt{ 16-48}}{2 }= \frac{4-\sqrt{ -32}}{2 }= \\\\= \frac{4-\sqrt{ 16*2}i}{2 }= \frac{4-4\sqrt{ 2}i}{2 }= \frac{2(2- 2\sqrt{ 2}i) }{2 }= 2- 2\sqrt{ 2}i

x_{2}=\frac{-b+\sqrt{b^2-4ac}}{2a}= \frac{4+\sqrt{ (-4)^2-4 \cdot1 \cdot12 }}{2 }=\frac{2(2+ 2\sqrt{ 2}i) }{2 }= 2+ 2\sqrt{ 2}i\\\\ If \ \sqrt{b^2-4ac} \ < \ 0, \\\\ then \ roots \ are \ \ imaginary .


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