Question

how many roots do the functions have in common? (roots, zeros, solutions all mean the same thing!) ( f(x)=x^{2}-8x + 16 ) ( y = g(x) ) f and g share no roots in common f and g share one root in common but each have another root that is not shared f and g share the same roots

Explanation:

Step1: Find roots of \(f(x)\)

Set \(f(x)=x^{2}-8x + 16=0\). Using the quadratic - formula \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\) for \(ax^{2}+bx + c = 0\), here \(a = 1\), \(b=-8\), \(c = 16\). Then \(\Delta=b^{2}-4ac=(-8)^{2}-4\times1\times16=64 - 64=0\). And \(x=\frac{8\pm\sqrt{0}}{2}=4\). So the root of \(f(x)\) is \(x = 4\).

Step2: Find roots of \(g(x)\) from graph

The graph of \(y = g(x)\) touches the \(x\) - axis at \(x = 4\). So the root of \(g(x)\) is \(x = 4\).

Answer:

f and g share the same roots