The biquadratic equation. Equations reducible to quadratic ones

An equation of the form ax⁴ + bx² + c = 0 (a ≠ 0) is called a biquadratic equation. We reduce it to the quadratic equation at² + bt + c = 0 with the substitution x² = t. After finding t₁ and t₂ we solve x² = t₁ and x² = t₂: if t > 0 then x = ±√t, if t = 0 then x = 0, and if t < 0 there is no real root. In a fractional equation we multiply both sides by the common denominator to get an integral equation; values that make a denominator zero are extraneous roots, so every root found must be checked against the denominators.