A **quartic equation** is the result of setting a quartic function to zero, an example quartic equation is the equation

- 2
*x*^{4}+4*x*³-26*x*²-28*x*+48=0,

*a*_{4}*x*^{4}+*a*_{3}*x*³+*a*_{2}*x*²+*a*_{1}*x*+*a*_{0}=0, and*a*_{4}≠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 a_{0}=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, a_{4}x³+a_{3}x²+a_{2}x+a_{1}=0.

Otherwise, divide the equation by *a*_{4}, to get an equation of the form

*x*^{4}+*ax*³+*bx*²+*cx*+*d*=0.

*t*^{4}+*pt*²+*qt*+*r*=0.