Question

2. I need help with question in the attached picture!

Answer 1

Option D is correct.

Explanation:

2x^2 -4x +9

We need to find root of the equation.

We will use quadratic equation to solve.

`x=(-b\pm√(b^2-4ac))/(2a)`

here a =2, b=-4 and c=9

Putting values and finding the value of x

`x=(-b\pm√(b^2-4ac))/(2a)\\x=(-(-4)\pm√((-4)^2-4(2)(9)))/(2(2))\\x=(4\pm√(16-72))/(4)\\x=(4\pm√(-56))/(4)\\x=(4\pm√(-(2*2*2*7)))/(4)\\x=(4\pm√(-(2^2*2*7)))/(4)\\x=(4\pm√(2^2)√(-14))/(4)\\We\,\,know\,\,√(-1)=i\,\,\\x=(4\pm2√(14)i)/(4)\\Dividing\,\,by\,\,4\,\,\\x= 1\pm(√(14)i)/(2) \\So,\\x=1+(√(14)i)/(2) \,\,and\,\, x=1-(√(14)i)/(2)`

So, one of the root is
`x=1+(√(14)i)/(2)`

So, Option D is correct.