which is a zero of the quadratic function f(x) = 16x² + 32x - 9?\no x = -5.25\no x = -2.25\no x = -1.25\no x…

Explanation:

Step1: Use quadratic - formula

For a quadratic function $ax^{2}+bx + c=0$ ($a = 16$, $b = 32$, $c=-9$), the quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. First, calculate the discriminant $\Delta=b^{2}-4ac$. $\Delta=(32)^{2}-4\times16\times(-9)=1024 + 576=1600$.

Step2: Find the roots

$x=\frac{-32\pm\sqrt{1600}}{2\times16}=\frac{-32\pm40}{32}$. For the plus - sign: $x=\frac{-32 + 40}{32}=\frac{8}{32}=0.25$. For the minus - sign: $x=\frac{-32-40}{32}=\frac{-72}{32}=-2.25$.

Answer:

$x=-2.25$ (corresponding to the second option)