Question

Find the real zeros and the number of x-intercepts. x^4 + 4x^2 + 4 = f(x)

Answer 1

\(x^4+4x^2+4\\=x^4+2x^2+2x^2+4\\=x^2(x^2+2)+2(x^2+2)\\=(x^2+2)(x^2+2)\)

Now \(f(x) = 0\) means \((x^2+2)(x^2+2)=0\) means \(x^2=-2\) which has no real solutions.

Answer 2

thank you so much