Question

which is a zero of the quadratic function f(x) = 16x² + 32x − 9?
○ x = −5.25
○ x = −2.25
○ x = −1.25
○ x = −0.25

Explanation:

Step1: Recall quadratic formula

For a quadratic equation \(ax^2 + bx + c = 0\), the solutions (zeros) are given by \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\). Here, \(a = 16\), \(b = 32\), \(c=-9\).

Step2: Calculate discriminant

Discriminant \(D=b^2 - 4ac=(32)^2-4\times16\times(-9)=1024 + 576 = 1600\).

Step3: Find square root of discriminant

\(\sqrt{D}=\sqrt{1600}=40\).

Step4: Compute zeros

\(x=\frac{-32\pm40}{2\times16}\).
First zero: \(x=\frac{-32 + 40}{32}=\frac{8}{32}=0.25\) (not in options).
Second zero: \(x=\frac{-32-40}{32}=\frac{-72}{32}=-2.25\).

Answer:

\(x = -2.25\) (the option is: \(x=-2.25\))