Question

Jonathan must determine the solutions of the quadratic equation

0=3x^2+2x+1
Which of the following is a solution to the equation?

Answer 1

B. -1-i sqrt2/3

Explanation:

A P EX

Answer 2

Answer: The correct option is (B)
`(-1-i\sqrt2)/(3).`

Step-by-step explanation: Given that Jonathan must determine the solutions of the quadratic equation :

`3x^2+2x+1=0.`

We are to select the correct solution to the above quadratic equation.

The solution of a quadratic equation of the form
`ax^2+bx+c=0,~a\\eq 0` is given by

`x=(-b\pm√(b^2-4ac))/(2a).`

In the given equation, we have

`a=3,~~b=2,~~c=1.`

Therefore, the solution of the equation is given by

`x\\\\\\=(-b\pm√(b^2-4ac))/(2a)\\\\\\=(-2\pm√(2^2-4*3*1))/(2*3)\\\\\\=(-2\pm√(4-12))/(6)\\\\\\=(-2\pm√(-8))/(6)\\\\\\=(-2\pm√(8i^2))/(6)~~~~~~~~~~~~~~~~~~\textup{since }i^2=1\\\\\\=(-2\pm2i\sqrt2)/(6)\\\\\\=(-1\pm i\sqrt2)/(3).`

So, the solutions of the given equation are

`x=(-1+i\sqrt2)/(3),~~~~~(-1-i\sqrt2)/(3).`

Out of the given options, a solution of the equation is
`(-1-i\sqrt2)/(3.)`

Option (B) is CORRECT.