Function g is defined by g(x)=3x^2-2x-5 What are the solutions to g(x)=0 x=-1 and x=(3)/(5) A x=1 and x=-(3)/(5) C x=-1 and x=(5)/(3) B x=1andx=-(5)/(3) D

To find the solutions to the equation $g(x)=0$, we need to solve the quadratic equation $3x^{2}-2x-5=0$.<br /><br />We can use the quadratic formula to solve this equation. The quadratic formula is given by:<br /><br />$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$<br /><br />In this case, $a=3$, $b=-2$, and $c=-5$. Plugging these values into the quadratic formula, we get:<br /><br />$x=\frac{-(-2)\pm\sqrt{(-2)^2-4(3)(-5)}}{2(3)}$<br /><br />Simplifying further, we have:<br /><br />$x=\frac{2\pm\sqrt{4+60}}{6}$<br /><br />$x=\frac{2\pm\sqrt{64}}{6}$<br /><br />$x=\frac{2\pm8}{6}$<br /><br />Therefore, the solutions to the equation $g(x)=0$ are:<br /><br />$x=\frac{2+8}{6}=\frac{10}{6}=\frac{5}{3}$<br /><br />$x=\frac{2-8}{6}=\frac{-6}{6}=-1$<br /><br />So, the correct answer is C: $x=-1$ and $x=\frac{5}{3}$.