Answer:
Option D is correct.
Step-by-step explanation:
2x^2 -4x +9
We need to find root of the equation.
We will use quadratic equation to solve.
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
here a =2, b=-4 and c=9
Putting values and finding the value of x
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-(-4)\pm\sqrt{(-4)^2-4(2)(9)}}{2(2)}\\x=\frac{4\pm\sqrt{16-72}}{4}\\x=\frac{4\pm\sqrt{-56}}{4}\\x=\frac{4\pm\sqrt{-(2*2*2*7)}}{4}\\x=\frac{4\pm\sqrt{-(2^2*2*7)}}{4}\\x=\frac{4\pm\sqrt{2^2}\sqrt{-14}}{4}\\We\,\,know\,\,\sqrt{-1}=i\,\,\\x=\frac{4\pm2\sqrt{14}i}{4}\\Dividing\,\,by\,\,4\,\,\\x= 1\pm\frac{\sqrt{14}i}{2} \\So,\\x=1+\frac{\sqrt{14}i}{2} \,\,and\,\, x=1-\frac{\sqrt{14}i}{2}[/tex]
So, one of the root is [tex]x=1+\frac{\sqrt{14}i}{2}[/tex]
So, Option D is correct.
