Question

the only solution of the equation $x^2 + bx + 16 = 0$ is $x = 4$. what is the value of $b$?
$\bigcirc$ $b = -16$
$\bigcirc$ $b = -8$
$\bigcirc$ $b = 8$
$\bigcirc$ $b = 16$

Explanation:

Step1: Substitute x = 4 into the equation

Substitute \( x = 4 \) into \( x^2 + bx + 16 = 0 \), we get \( 4^2 + b\times4 + 16 = 0 \).

Step2: Simplify the equation

Calculate \( 4^2 = 16 \), so the equation becomes \( 16 + 4b + 16 = 0 \). Combine like terms: \( 32 + 4b = 0 \).

Step3: Solve for b

Subtract 32 from both sides: \( 4b = -32 \). Then divide both sides by 4: \( b = -8 \).

Answer:

\( b = -8 \) (corresponding to the option "b = -8")