which is a zero of the quadratic function f(x) = 4x² + 24x + 11?\no x = -9.25\no x = -5.5\no x = 0.5\no x =…

Explanation:

Step1: Use quadratic formula

For a quadratic function $ax^{2}+bx + c = 0$ ($a\neq0$), the quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. In $f(x)=4x^{2}+24x + 11$, we have $a = 4$, $b = 24$, and $c = 11$.

Step2: Calculate the discriminant $\Delta=b^{2}-4ac$

$\Delta=(24)^{2}-4\times4\times11=576 - 176=400$.

Step3: Find the roots

$x=\frac{-24\pm\sqrt{400}}{2\times4}=\frac{-24\pm20}{8}$. First root: $x_1=\frac{-24 + 20}{8}=\frac{-4}{8}=-0.5$. Second root: $x_2=\frac{-24-20}{8}=\frac{-44}{8}=-5.5$.

Answer:

$x=-5.5$ (corresponding to the second option)