Solution of biquadratic equations

Biquadratic equations are a special case of highly demanded in mathematical, statistical, and engineering calculations 4th-degree equations of the form
F (x) = a x 4 + a x 3 + c x2 + d x + e, where the condition is ensured: «a» should not be equal to zero. Biquadratic equations are equations of the form
ax4 + bx2 + c = 0.

Online calculator for substitution of a new variable y = x 2 converts a biquadratic equation into a quadratic one, using the initial data in the form of coefficients given in the appropriate fields a, b and c solves it. As a result, roots are found y1 and y2, which are substituted into y = x 2. And the roots of the biquadratic equation are issued upon its solution.

How much more complicated and slower it is to solve manually than with the help of an online calculator can be considered with an example. Set coefficients 4, (-5) and 1 equation 4x4 - 5x2 + 1 = 0 in the appropriate fields, press «calculate». On all about everything for obtaining the result x1 = 1, x2 = - 1, x3 = 0,5, x4 = - 0.5 spent 15 seconds.