Question

How many x intercept appear on the graph of the polynomial function F(x)=x4-5x2


Help on this one

Answer 1

$f(x)=x^4-5x^2\\\\x^4-5x^2=0\\\\x^2(x^2-5)=0\\\\x^2[x^2-(\sqrt5)^2]=0\\\\x^2(x-\sqrt5)(x+\sqrt5)=0\iff x=0\ \vee\ x=\sqrt5\ \vee\ x=-\sqrt5$

Answer: 3 x-intercepts.