Question

Jonathan must determine the solutions of the quadratic equation

Answer 1

Answer:  The correct option is (B) $\dfrac{-1-i\sqrt2}{3}.$

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 $ax^2+bx+c=0,~a\neq 0$ is given by

$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}.$

In the given equation, we have

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

Therefore, the solution of the equation is given by

$x\\\\\\=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\\=\dfrac{-2\pm\sqrt{2^2-4\times3\times1}}{2\times3}\\\\\\=\dfrac{-2\pm\sqrt{4-12}}{6}\\\\\\=\dfrac{-2\pm\sqrt{-8}}{6}\\\\\\=\dfrac{-2\pm\sqrt{8i^2}}{6}~~~~~~~~~~~~~~~~~~\textup{since }i^2=1\\\\\\=\dfrac{-2\pm2i\sqrt2}{6}\\\\\\=\dfrac{-1\pm i\sqrt2}{3}.$

So, the solutions of the given equation are

$x=\dfrac{-1+i\sqrt2}{3},~~~~~\dfrac{-1-i\sqrt2}{3}.$

Out of the given options, a solution of the equation is $\dfrac{-1-i\sqrt2}{3.}$

Option (B) is CORRECT.

Answer 2

Answer:

I think it is C