Question

f(x) = 4x² + 16x + 9.

Answer 1

You have the following function:

$f(x)=4x^2+16x+9$

In order to find the zeros of the previous function, use the quadratic formula:

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

In this case you have:

a = 4

b = 16

c = 9

replace the previous values into the quadratic formula:

$\begin{gathered} x=\frac{-(16)\pm\sqrt[]{(16)^2-4(4)(9)}}{2(4)} \\ x=\frac{-16\pm\sqrt[]{112}}{8} \\ x=\frac{-16\pm10.58}{8} \end{gathered}$

Then, you have the following values for x:

$\begin{gathered} x_1=\frac{-16+10.58}{8}=-\frac{5.42}{8}=-0.67\approx-0.7 \\ x_2=\frac{-16-10.58}{8}=-\frac{26.58}{8}=-3.32\approx-3.3 \end{gathered}$

Hence, the solution to the given function are:

x1 = -0.7

x2 = -3.3