Question

Using the quadratic formula, determine which type of solutions the given quadratic equation will have. 3x2 + 24x + 33 = 0 OA. 2 complex solutions OB. 1 complex solution OC. 2 real solutions OD. 1 real solution

Answer 1

Given the quadratic equation:

`3x^2+24x+33=0`

Dividing this equation by 3:

`x^2+8x+11=0`

The general solution, given by the quadratic formula, is:

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

From the equation, we identify:

`\begin{gathered} a=1 \\ b=8 \\ c=11 \end{gathered}`

Now, we analyze the term inside the square root:

`b^2-4ac=8^2-4\cdot1\cdot11=64-44=20>0`

Since this term is positive, then the solutions are real.

Answer: C. 2 real solutions