find value(s) of for which f(x) = g(x).

Question

f(x) = x^4 - 2x^2, g(x) = 2x^2

Answer 1

f(x) = g(x)

x^4 - 2x^2 = 2x^2

x^4 -4x^2 = 0

x^2(x^2 -4) = 0

x^2(x+2)(x-2) = 0

x = 0, -2, +2

any 4th degree polynomial has 4 solutions, so you could say

x = 0, 0, -2, +2

the x=0 root has multiplicity 2, 0 repeats. If you graphed it, it would be tangent to the x axis at x=0 and cross the x axis at -2 and +2

Answer 2

Just need to set f(x) = g(x) and solve for x.

x⁴-2x²=2x²

x⁴-4x²=0

x²(x²-4)=0

x²(x+2)(x-2)=0

x = 0, 2, -2