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Algebra · Polynomial-Equations

Solve x^4 - 5x^2 + 4 = 0

x^{4} - 5 x^{2} + 4 = 0

Step by step

  1. x^{4} - 5 x^{2} + 4 = 0

    Start from the equation as given.

  2. \left(x - 2\right) \left(x - 1\right) \left(x + 1\right) \left(x + 2\right) = 0

    Factor the polynomial (rational-root test + division).

  3. x + 1 = 0 \;\Rightarrow\; -1

    Set each factor equal to zero and solve it.

  4. x - 1 = 0 \;\Rightarrow\; 1

    Set each factor equal to zero and solve it.

  5. x - 2 = 0 \;\Rightarrow\; 2

    Set each factor equal to zero and solve it.

  6. x + 2 = 0 \;\Rightarrow\; -2

    Set each factor equal to zero and solve it.

  7. x = -1 ,\; x = 1 ,\; x = 2 ,\; x = -2

    All 4 roots.

Reveal the answer
x = -1 ,\; x = 1 ,\; x = 2 ,\; x = -2