how to solve a biquadratic equation

Hello student,
Please find the answer to your question below
Equation of the formax⁴+bx²+c=0, wherea≠0is calledbiquadratic.
Biquadratic equations is solved with method of introducing new variable:
settingx²=y, we obtain quadratic equationay²+by+c=0.
Example. Solve equationx⁴+4x²−21=0.
Letx²=y, then we obtain quadratic equationy²+4y−21=0.
Solutions of this equation are x=-7 and x=3.
Recall, thatx²=y, therefore we have set of equations:x²=−7,x²=3.
First equation doesn't have roots, second has two roots:
These two roots will be roots of the initial equation