Given:
The quadratic equation is
[tex]0=-3x^2-4x+5[/tex]
To find:
The simplest radical form of the solution.
Solution:
Quadratic formula:
If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
We have,
[tex]0=-3x^2-4x+5[/tex]
Here, a=-3, b=-4 and c=5. Putting these values in the quadratic formula, we get
[tex]x=\dfrac{-(-4)\pm \sqrt{(-4)^2-4(-3)(5)}}{2(-3)}[/tex]
[tex]x=\dfrac{4\pm \sqrt{16+60}}{-6}[/tex]
[tex]x=\dfrac{4\pm \sqrt{76}}{-6}[/tex]
[tex]x=\dfrac{4\pm 2\sqrt{19}}{-6}[/tex]
Taking 2 common, we get
[tex]x=\dfrac{2(2\pm \sqrt{19})}{-6}[/tex]
[tex]x=\dfrac{(2\pm \sqrt{19})}{-3}[/tex]
[tex]x=-\dfrac{(2\pm \sqrt{19})}{3}[/tex]
Therefore, the correct option is A.
