Show your work Use calculus to show that the equation x4 6x

Show your work!

Use calculus to show that the equation x4 + 6x2 = 1 has exactly two real solutions.

Solution

f(x) = x⁴ + 6x² -1 =0

f\'(x) = df(x)/dx = 4x³ + 12x = 4x(x² +1)

here f\'(x) = 0 has only a single solution which is x=0

therefore f(x) will have exactly two roots on either side of x=0.