Biquadratic Equations
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
x4 − 10x2 + 9 = 0
x4 − 10x2 + 9
x2 = t
x4 − 10x2 + 9 = 0
t2 − 10t + 9 = 0
x4 − 61x2 + 900 = 0
x4 − 25x2 + 144 = 0
x4 − 16x2 − 225 = 0
