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how to solve a biquadratic equation

how to solve a biquadratic equation

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1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
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:\pm \sqrt{3}
These two roots will be roots of the initial equation

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