<span>The number of x-intercepts that appear on the graph of the function </span>f(x)=(x-6)^2(x+2)^2 is two (2): x=6 (multiplicity 2) and x=-2 (multiplicity 2)
Solution x-intercepts: f(x)=0→(x-6)^2 (x+2)^2 =0
Using that: If a . b =0→a=0 or b=0; with a=(x-6)^2 and b=(x+2)^2
(x-6)^2=0 Solving for x. Square root both sides of the equation: sqrt[ (x-6)^2] = sqrt(0)→x-6=0 Adding 6 both sides of the equation: x-6+6=0+6→x=6 Multiplicity 2
(x+2)^2=0 Solving for x. Square root both sides of the equation: sqrt[ (x+2)^2] = sqrt(0)→x+2=0 Subtracting 2 both sides of the equation: x+2-2=0-2→x=-2 Multiplicity 2
