Given the quadratic equation:
[tex]3x^2+24x+33=0[/tex]Dividing this equation by 3:
[tex]x^2+8x+11=0[/tex]The general solution, given by the quadratic formula, is:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]From the equation, we identify:
[tex]\begin{gathered} a=1 \\ b=8 \\ c=11 \end{gathered}[/tex]Now, we analyze the term inside the square root:
[tex]b^2-4ac=8^2-4\cdot1\cdot11=64-44=20>0[/tex]Since this term is positive, then the solutions are real.
Answer: C. 2 real solutions
