Using the quadratic formula, what are the solutions to $3x^2-12x+24=0$?

• A. $x=2$
• B. $x=2\pm 2i$
• C. $x=2\pm 2$
• D. $x=4\pm 2i$

Answer: (B)

Verified step by step guidance

1. Identify the coefficients from the quadratic equation \$3x^{2} - 12x + 24 = 0\(. Here, \)a = 3\(, \)b = -12\(, and \)c = 24$.
2. Recall the quadratic formula for solving \(ax^{2} + bx + c = 0\): \[x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}\]
3. Calculate the discriminant \(\Delta = b^{2} - 4ac\) using the values of \(a\), \(b\), and \(c\). This will determine the nature of the roots (real or complex).
4. Substitute the values of \(a\), \(b\), and \(c\) into the quadratic formula, including the discriminant, to write the expression for the roots.
5. Simplify the expression under the square root and the entire formula to express the solutions in the form \(x = \text{real part} \pm \text{imaginary part} \times i\) if the discriminant is negative.