Question

What are the zeros of the polynomial function? f(x)=x2−16x+48 Enter your answers in the boxes.

Answer 1

Answer:

$x_{1,2}=4,\ 12$

Step-by-step explanation:

Consider the polynmial function $f(x)=x^2-16x+48.$  The zeros of the polynomial function are the values of x at which f(x)=0. Solve the equation $x^2-16x+48=0:$

$D=b^2-4ac=(-16)^2-4\cdot 1\cdot 48=256-192=64=8^2,\\ \\x_{1,2}=\dfrac{-b\pm \sqrt{D}}{2a}=\dfrac{-(-16)\pm \sqrt{64}}{2\cdot 1}=\dfrac{16\pm 8}{2}=4,\ 12.$