A quartic equation is the result of setting a quartic function to zero, an example quartic equation is the equation
- 2x4+4x³-26x²-28x+48=0,
- a4x4+a3x³+a2x²+a1x+a0=0, and a4≠0.
It is the highest degree of polynomial equation for which exact values of the roots can be found, by taking nth roots, and use of the normal algebraic operators.
If a0=0, then one of the roots is x=0, and the other roots can be found, by dividing by x, and solving the resulting cubic equation, a4x³+a3x²+a2x+a1=0.
Otherwise, divide the equation by a4, to get an equation of the form
- x4+ax³+bx²+cx+d=0.
- t4+pt²+qt+r=0.