How to solve x^4-3x+20

Answer 1

there are no real solutions

try graphing it. Use a graphing calculator. Or just plot a few points to get the general idea of the curve.

It never intersects the x axis. with no x intercepts, there are no real solutions.

but a 4th degree equation has 4 potential solutions. In this case they're all imaginary.

Two pairs of conjugate pairs.

take the derivative to find the turning point(s)

y' = 4x^3 -3 = 0

x^3 = 3/4

x= cube root of 3/4 that's the x coordinate of the minimum point or vertex of the curve (the other 2 solutions are imaginary)