RConics (version 1.1.2)

cubic: Roots of the cubic equation.

Description

Return the roots of a cubic equation of the form \(ax^3 + bx^2 + cx + d=0\).

Usage

cubic(p)

Value

A vector corresponding to the roots of the cubic equation.

Arguments

p

a \((4 \times 1)\) vector of the four parameters \((a, b, c, d)\) of the cubic equation.

Examples

# cubic equation x^3 - 6x^2 + 11x - 6 = 0
# parameter
b <- c(1,-6, 11, -6)

# roots
x0 <- cubic(b)

# plot
x <- seq(0,4, by=0.001)
y <- b[1]*x^3 + b[2]*x^2 + b[3]*x + b[4]

# plot
plot(x,y,type="l")
abline(h=0,v=0)
points(cbind(x0,c(0,0,0)), pch=20,col="red",cex=1.8)