Question

How would you find the zero of f (x)=16x^4 - 9x^2

Answer 1

$f(x)=16x^4-9x^2\\\\f(x)=0\iff16x^4-9x^2=0\\\\x^2(16x^2-9)=0\iff x^2=0\ \vee\ 16x^2-9=0\\\\x=0\ \vee\ 16x^2=9\\\\x=0\ \vee\ x^2=\frac{9}{16}\\\\x=0\ \vee\ x=-\sqrt\frac{9}{16}\ \vee\ x=\sqrt\frac{9}{16}\\\\x=0\ \vee\ x=-\frac{3}{4}\ \vee\ x=\frac{3}{4}$

Answer 2

$f (x) = 16x ^ 4 - 9x ^ 2 \\ \\16x ^ 4 - 9x ^ 2=0\\ \\x^2(16x^2-9)=0 \\ \\x^2 =0 \ \ or \ \ 16x^2-9=0\\ \\ x=0 \ \ or \ \ (4x-3)(4x+3)=0\\ \\ x=0 \ \ or \ \ 4x-3=0 \ \ or \ \ 4x+3 =0\\ \\x=0 \ \ or \ \ 4x=3 \ \ / :4 \ \ or \ \ 4x=-3\ \ / :4 \\ \\ x=0 \ \ or \ \ x=\frac{3}{4} \ \ or \ \ x=-\frac{3}{4}$