Consider the quartic y x4 x2 a for which values of a does

Question

1. Consider the quartic y = x⁴ +x² +a. For which values of a does the equation have two real roots?

2. Plot on the same graph the functions f(x) = x + 3, g(x) = x² + 1, f(x)g(x) and f(x)/g(x) for the range x ∈ [-1, 1]. (You need to decide how many points to use to get a smooth curve, and whether to set up the vector x either using the colon construction or linspace). You also need to remember to use dot arithmetic since you are operating on vectors.