Question

what are the zeros of f?f (x) = x² + 8x + 12A) 2 and 6B) 3 and 4 C) -3 and -4D) -2 and -6

Answer 1

To find the zeros of f(x), follow the steps below.

Step 01: Use the quadratic formula.

For a quadratic equation y = ax² + bx + c, the zeros are:

$\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \end{gathered}$

Step 02: Substitute the coefficients of f(x) in the quadratic formula.

For f(x) = x² + 8x + 12, the formula is:

$x=\frac{-8\pm\sqrt[]{8^2-4\cdot1\cdot12}}{2\cdot1}$

Step 03: Solve the quadratic formula.

$\begin{gathered} x=\frac{-8\pm\sqrt[]{64^{}-48}}{2} \\ x=\frac{-8\pm\sqrt[]{16}}{2} \\ x=\frac{-8\pm4}{2} \end{gathered}$

And finally, find the zeros:

$\begin{gathered} x_1=\frac{-8-4}{2}=-\frac{12}{2}=-6 \\ x_2=\frac{-8+4}{2}=-\frac{4}{2}=-2 \end{gathered}$

Answer: D) The zeros are -2 and -6.