Biquadratic equations (3º- 4º ESO)

Biquadratic equations are quartic equations with no odd-degree terms:

ax4 + bx2 + c = 0

Solving Biquadratic Equations

To solve biquadratic equations, change x2 = t, x4 = t2; this generates a quadratic equation with the unknown, t:

at2 + bt + c = 0

For every positive value of t there are two values of x, find:

The same procedure can be used to solve the equations of the type:
ax6 + bx3 + c = 0                        ax8 + bx4 + c = 0                           ax10 + bx5 + c = 0

Examples: